If reference frames are equally valid, then why do teachers say the geocentric view is wrong? If all reference frames are valid, then why is the geocentric model taught as "wrong" in schools?
I've checked many websites but none of them clear the issue. Wiki says that in relativity, any object could be regarded as the centre with equal validity. Other websites and answers make a point on the utility of the heliocentric model (simplicity, Occam's razor...) but just because something is not so easy to deal with doesn't mean it is wrong.
Note: I am not asking for evidence that geocentrism is wrong; I am asking for a way to resolve the contradiction (from what I see) between relativity and this "geocentricism is wrong" idea.
 A: A flippant way of addressing this question is to say: size matters.

We organize our understanding of celestial motion in an ascending scale, recognizing gravitationally bound systems at ever larger sizes.
The Earth and the Moon are orbiting their common center of mass. But the Earth is so much heavier than the Moon that this common center of mass is actually so close to the center of the Earth that it is beneath the surface of the Earth.
The Earth-Moon system is orbiting the center of mass of the Solar System.

At this point let me point out which things in theory of motion carried over from newtonian mechanics to General Relativity. The notion of common center of mass carries over from newtonian mechanics to GR.
(Some people may argue as follows: if you are an astronaut in a spacecraft without windows, orbiting a celestial body, then locally you cannot tell whether the spacecraft is orbiting a celestial body, or whether the spacecraft is moving in a straight line in interstellar space. While that is true, it has no bearing on how to assess gravitationally bound systems at scale. In any form of science one must take all the relevant information into consideration. If an observer is deprived of some of the relevant information (not having windows) then the information value of that observer's observations extend only as far as that observer can see. There is no exception to the following rule: in science one must always take all the relevant information into account. Conversely: depriving yourself of information is never beneficial.)

The celestial bodies of the Solar system are orbiting the common center of mass of the Solar system. Jupiter is in fact sufficiently heavy such that the common center of mass of the Sun and Jupiter is not inside the Sun.
The next level up in gravitationally bound system is our Galaxy; Solar system is orbiting the center of mass of our Galaxy.
The next level up is a cluster of Galaxies. In Astronomy Galaxies are considered gravitationally bound when it can be inferred from their relative velocity that the gravitational attraction is in the process of overcoming the overall expansion of the Universe.
A: Decades ago, Martin Gardner wrote an article about hollow-earth cosmology. Relevant to this question is his discussion of the hollow-earth model of Mostafa A. Abdelkader.

[H]e gives to the concave-earth model a mathematical precision lacking in all earlier accounts. Imagine the earth's surface to be a perfect sphere. Using simple equations, Abdelkader performs on space what geometers call an "inversion" with respect to the sphere. All points outside the sphere are exchanged with all points inside. The sphere's center maps to infinity, and infinity maps to the center. [...]
After inverting the cosmos, Abdelkader then applies the same inversion to all the laws of physics. The result is a consistent physics that cannot be falsified by any conceivable observation or experiment! Of course the equations for the laws become horribly complex. Light rays follow circular arcs, the velocity of light goes to zero as it approaches the center of inversion, and all sorts of other bizarre modifications of laws are required. [...] Instead of the earth rotating, the shrunken celestial bodies revolve the opposite way around the earth's "axis." Because light follows curved paths, the sun seems to set as usual below the "horizon" as it travels a conical helix, six months in one direction and six months in the other. The Foucault pendulum, Coriolis effects, and other inertial "proofs" of the earth's rotation are all accounted for by the drastically modified laws.

Abdelkader's model is really just the standard model in nonstandard coordinates. His coordinate system isn't wrong, but it is very inconvenient. To prefer his coordinates, you would have to believe that the earth really is hollow in some scientifically undetectable way, and that working in certain coordinates brings us mystically closer to that reality. To prefer heliocentric coordinates, you don't need to have any such metaphysical beliefs. You just need to not be a glutton for punishment.
Though geocentric coordinates aren't wrong as such, I would say that heliocentrism is really more correct than geocentrism. The fact that the laws of physics have a simpler form in heliocentric coordinates implies that the intrinsic, coordinate-independent shape of spacetime has a structure that is a better fit to heliocentric coordinates. The world-tube of the earth really does have a helical shape that the world-tube of the sun does not, although I don't know how to make that precise.
A: "Geocentric model" is a loaded term. It's not just referring to the the sun rotating around the Earth. If you are only concerned with whether the sun orbits the Earth or whether the Earth orbits the sun it's a wash. It is referring to the model as whole which must explain all the observed phenomena seen. This includes things such as why the retrograde motion of planets where they changes direction in the sky, or the phases of Venus.
Despite all the additional complexity of concentric circles and such that were introduced to the geocentric model it was never able to adequately explain some of these, whereas the heliocentric model did, and with much less complexity.
A: You're right that in general relativity any frame of reference can be accommodated. That said, some frames of reference are more convenient than others in terms of simplifying the description of all the phenomena. And by "convenient" I mean the difference between requiring a modern computer to handle and could be done with pencil and paper hundreds of years ago. I mean, I could speak in binary by spelling out my words in ascii, but it's darn inconvenient, no? Well the difference in level of convenience here is on that level. In other words, the difference in effort needed to use one model makes it objectively wrong to use, even if it is technically possible to do.
If you're interested in things happening on or near the surface of the Earth, then a geocentric reference frame is absolutely the simplest and most effective way to go. The only observable effects of Earth's motion that I'm aware of at this level are the oblateness of the Earth and the large scale patterns in the wind caused by the Coriolis effect. Even going out as far as the moon, geocentric is the way to go.
If, however, you want to describe what's going on the in the solar system, heliocentric really is much much simpler. Something like 98% of the mass of the solar system is in the sun, and most of the rest is in Jupiter, so the orbits are very well approximated by ellipses in this reference frame. Showing that orbits are ellipses is an exercise simple enough that we can have undergraduates do it. If I had to work everything out in a geocentric reference frame, without just transforming back from the heliocentric one, I suspect I would have to rely on numerical integration on a computer.
Likewise, explaining the apparent motion of the sun through the stars over the course of a year is much easier in a heliocentric model. The Earth is rotating and conservation of angular momentum means that its axis of rotation is (nearly) constant in direction, so as it orbits around the sun the angle between the sun's rays and the Earth's equator changes as a consequence. In a geocentric frame the "fictitious forces" all balance delicately to have the sun barreling around the Earth at insane speeds every day, and bouncing around between the limits of the tropics as it gets closer and farther. It's much simpler to describe and understand as the earth rotates on an axis, and orbits in a ellipse.
Going outward to the Milky Way, a heliocentric frame makes less sense. There you want to work in galactocentric coordinates. Going out further still, on the cosmic scale you really need CMB coordinates.
Long story short, you use the right coordinate system for the job at hand, where "right" is dictated by ease of calculation and description in reproducing all observed phenomena.
A: If 'geocentrism' means that you can regard the Earth as stationary and describe the motion of Sun and planets accordingly, then geocentrism isn't wrong.
But if 'geocentrism' means that The Sun and planets have simple (for example circular) orbits about the Earth, then it is wrong. Almost 2000 years Ago, Ptolemy knew that a geocentric solar system based on circles needed the planets to move in circles nested on circles nested on circles in order for theory to match observation – which for some planets even involves their stopping and going backwards for a while. [The nested circle treatment is analogous to a Fourier analysis of a complicated shape of orbit.]
A heliocentric system based on circles rather than ellipses still needs these 'epicycles', but smaller ones and fewer of them. I'd add that I think it's perfectly reasonable to teach children that the Earth and other planets "go round the Sun". There's no reason, though, to say to them that the Sun, any more than the Earth, is stationary.
A: Sean Carroll wrote a blog post about this exact queston years ago: https://www.preposterousuniverse.com/blog/2005/10/03/does-the-earth-move-around-the-sun/.
As Sean E. Lake says, it's perfectly true that the Sun goes around the Earth ... in some reference frame. And that reference frame is actually a quite convenient one to use to describe many terrestrial physics situations. But it's very inconvenient to use that reference frame for solar-system-scale calculations, because it is not anywhere close to an inertial global frame even in the Newtonian limit.
A: It isn't the case that General Relativity means that all reference frames are equally valid. This is a common mistake.
General Relativity says that the everyday phenomenon we call gravity is due to two things: 1) free fall in a uniform (i.e. not changing according to position) gravitational field is actually an inertial frame, and 2) tidal forces, where gravity does actually vary according to position (e.g. stronger closer to the centre of mass), leading to curvature of spacetime.
That curvature can't be transformed away by any coordinate transform. It's an invariant.
So a Solar System observer is quite entitled to choose a geocentric reference frame if they wish, but they'll have this mysterious curvature to explain.
Conversely, if instead they use a heliocentric model, they will understand the Solar System as a gravitational system dominated by the Sun's mass curving the spacetime around it.
Note that, whilst important, this isn't just a matter of parsimony. It isn't just that the geocentric way of thinking is more convoluted or bizarre. It's that we actually have two very good models (GR and the Standard Model) that explain the vast majority of how the stuff in our Solar System behaves. Obviously there are still problems; still, in general we should prefer theories that are not just more parsimonious, but also act as a cohesive, integrated framework, as GR does with the idea that matter curves spacetime and this curvature explains how matter moves.
Now, it'd be perfectly reasonable to take from GR that globally, both heliocentrism and geocentrism are "wrong", as no local frame is globally valid. However, this would ultimately be dismissing the question ("does the Earth go round the Sun?") altogether as meaningless, rather than saying both answers are valid. Geocentrism is thus wrong in either case.
A: The geocentric model is taught as "wrong" in schools because it is.
Sure, you're welcome to consider the Earth as the center of the universe.  And in that reference frame, the Sun orbits the earth.  But once you have made that decision, you must be consistent. Don't forget that you need to consider the other planets, too.
According to the classic, Ptolemaic view of the universe, the Sun orbits the earth, but also all the other planets orbit the earth directly, without also orbiting the Sun:
Wikipedia graphic of Ptolemaic, geocentric view of the Solar System
The image linked above shows the Sun in its own, independent orbit about the earth, while the other known plants do not orbit the Sun.  That is why the Ptolemaic view is wrong.
The image linked above is obviously a modern-day interpretation. If you are looking for something more primary, consider these images:

*

*Drawing from an Icelandic manuscript dated around 1750 illustrates the geocentric model.

*Ptolemaic view of the Universe 1539
Even if you consider the earth to be the center of the universe, the other planets do not orbit the earth directly.  They only orbit earth only by virtue of orbiting the sun (which in turn orbits the earth).
I am not a historian of science.  It's possible that there was a subsequent, non-Ptolemaic, geocentric view in which the earth is the center of the universe, the Sun orbits the Earth, and the other planets orbit the Sun as it goes around the Earth.  If that is the case, that view is not necessarily "wrong." As other answers have pointed out, it is just absurdly more complicated than a heliocentric view of the Solar System.
A: Physics doesn't depend on the observer
Different descriptions don't change Physics.
You can just use the simplest description (coordinates, reference frames, ...) for your needs, and change to another one via coordinate and reference transformation rules that preserve the invariant nature of the physical process w.r.t. the observer.
A "good" physical theory/model/description:

*

*is a simple theory/model/description, where simple really means you need the smallest amount of calculations or the easiest calculation as possible

*provides good results when compared with experimental observations within the accuracy needed by the events described

Short story of theories about the motion of the solar system
Prehistory. (Pre)historically, humans were mainly interested in the motion of the Sun and the Moon, and the geocentric system looks quite a natural choice for the description of the system Earth-Sun-Moon. The background of the fixed stars fits this model quite naturally as well.
In the ancient Mesopotamia, the first planets were discovered as celestial bodies "moving differently" if observed from the Earth. Anyway, they were good enough in Math to correctly describe the motion of the planets using a geocentric point of view, and they probably were not so much interested in a easier way to describe their motion, since they were not so affected by them, probably excluding for religion reasons.
First heliocentric models. Around 300 B.C., Greeks astronomer Aristarchus of Samos identified that planets describe orbits around the Sun (however you describe it, planets orbit around the Sun, or the Sun orbits around the planets, the description is relative, the Physics is not), presenting its heliocentric model where planets described circular orbits around the Sun. Anyway, this theory suffered from substantial errors and didn't provide accurate enough predictions: inaccurate predictions and accusations of heresy were enough to keep the geocentric theory alive for some centuries. He had formulated a qualitatively good theory, but not a quantitative good theory (simple model, but not accurate results).
Galileo and Kepler. The use of telescope in '400-'500 provided an instrument for more detailed astronomical observations, that allowed:

*

*Galileo to observe Jupiter satellites, making him think about if that system could somehow resemble Earth-Moon system;

*Kepler to formulate and accurately test its 3 laws about planetary motion. These three laws provided quite a simple physical model capable of doing accurate predictions of the motion of celestial bodies, if compared with the results of the geocentric theories, thus a good theory (simple description + accurate results).

After that a good heliocentric theory was available, discussions that followed about helio- or geocentrism in '500-'600 were more about philosophy, religion and the role of the human beings in the universe and the history.
Newton's classical mechanics as the first theory of gravitation, through action at disance. During plague lockdown of the 1666 in England, an undergrad student named Newton developed differential calculus for formulating the three principles and developing its theory about Mechanics, including gravity as an action at distance described by its universal gravitation law,
$\mathbf{F} = G m M\dfrac{\mathbf{r}}{r^3}$
Limit of Kepler's laws and classical mechanics: precession of the Mercury perihelium. Kepler's laws are good enough for many applications in celestial motion, but they are not good enough to describe the precession of Mercury perihelium, the closed point of the orbit from the Sun.
We're dealing with a very small prediction error made by classical mechanics and Kepler's laws, about $42.9799$ arcsec/century.
This is one of the classical tests for the validation of Einstein's general relativity, that manages to provide this (more) accurate results, promoting it as the most accurate theory of gravitation, and thus for the motion of celestial objects.
A: In the strictest sense, geocentrism, heliocentrism and all other centrisms (the universe revolves around my teacup) are equivalent, as you say. The geocentrism vs heliocentrism discussion is more relevant to the history and philosophy of science than modern physics.
