Why do we theorize that the Big Bang created space? I just asked this astronomy question about how far away the light is that would show us the beginning of time, the Big Bang. 
Some answers claim that the light I ask about doesn't exist, because "The Big Bang created space and time."
The way I see it, space, true "space" is literally nothing. You can't create nothing. So I would argue that the BB didn't create space, but only filled it. 
Can someone please explain why we theorize that space itself was created by the Big Bang? 
 A: If you had empty space and then matter expanded from a point in it, then some of the matter would be in the center, seeing everything moving away from it.  Some of it would be near the edge and see darkness filling half their world.
We see matter moving away, and it seems unlikely that we just happen to be so close to a center of the universe.  So we look for other options that don't require us to be in such a special place.  Since we already know that space and time can be curved, when we look for other options, there are lots of really interesting options.
If the universe were 1d you could imagine that at different times, the universe is a circle, later times it is a larger circle.  So the radial direction is time, and space goes around in a circle.  So what we expand into is ... the future.
If the universe were 2d you could imagine that at different times, the universe is the surface of a sphere, later times it is the surface of a larger sphere.  So the radial direction is time, and space goes around in a spherical shell.  So what we expand into is ... the future.
Since the universe is 3d we can imagine that at different times, the universe is the surface of a hypersphere, later times it is the surface of a larger hypersphere.  So the radial direction is time, and space goes around in a hyperspherical shell.  So what we expand into is ... the future.
The advantage of these models is that every point in the universe at a particular time is treated equally.  We can then put in specific details about how quickly it expands, the matter and radiation and other fields in it and see what predictions it makes.  If it agrees with what we see, we like it but keep checking.  If it doesn't agree, then we try to fix it, look for errors, and consider alternatives.
Having the expansion be into the future is nice because that is what happens if you wait.  Any part of the universe ends up in future, so maybe the future is just bigger than the present.  But if you run that reasoning backwards, the universe used to be smaller in the past.  Maybe it contracts towards a point, or maybe something interesting happened when it was small.
It's an area of active research.
A: 
"The way I see it, space, true "space" is literally nothing"

Most physicists and I believe many philosophers would disagree. The notion of "Nothing" is impenetrable logically: "nothing" has neither any properties nor relationships with anything else  that can be reasoned about. The best you could do would be to assert that "nothing" is somewhat like the empty set: an initial object in a category of things that we want to talk about in physics. Karl Popper, a fashionable icon to cite in modern science, would berate you for including "nothing" in science because, having no properties, one cannot make potentially falsifiable statements about "nothing" .
In stark contrast, "empty space" definitely has properties. General Relativity shows us that empty space is inhomogeneous: the curvature we compute in this piece of empty spacetime here can be decidedly different from that of that piece over there. I'd like to restate Lionel Brits's answer in even more emphatic terms: empty space is not only filled with quantum fields, it is made of quantum fields. We call it "empty" locally when we drive it into its lowest energy state or ground state. We can do this by locking it up in a radiation shielded box and pumping all the molecules out. 
If the universe is a so called compact, boundaryless manifold like a higher dimensional analogue of a 2-sphere or the surface of a balloon, then nothing exists aside from the Universe. There is no outside, and the mathematical fields of things like topology and geometry - especially differential geometry - give us the language we need to describe such a thing with no reference to anything outside. One doesn't need to think of these things as embedded in any "outside".

User Chris White makes a comment worth capturing in an answer:


...I feel like pointing out that one doesn't need quantum fields for space to be non-nothingness. Even the anti-absolute-Newtonian-space camp would say space is the set of relations between objects, and those relations are not arbitrary. Even if there were no proper objects in the universe, for there to even be the ability to hypothesize objects with a spatial relation to one another, space must in some sense exist and have properties. 

as does user Stan Liou:

I think that you're insufficiently emphatic. Even a simple Euclidean space has nontrivial structure, such as notions of distance and straightness. One of the main points of GTR is the marriage of physical inertial properties and the notion of straigness (generalized to affine geodesics), your point is morally true classically as well. (ETA: heh, ninjas.) 

A: According to inflation, strictly speaking, space is still being created. I find this idea very interesting. Also, the idea of space as being an empty void to be filled is out of date. Space is full of fields, even when there are no particles present.
A: Your question is: why is said that the space  is expanding ?
The answer that everyone are aware, by consensus :
We see a reddening of the light received from distant stars and galaxies for the same stellar processes we see in the sun and nearby stars. One way to interpret it, the official way, the only one that your teacher and scientists do know, is: the galaxies are moving away from us in every direction.  The space expansion and the BB theory began. 

But I've a different description for the same observations, not requiring space expansion:
We measure with atoms and, in all the building of physics, there are not a single word about the 'absolute' size of the atom (I welcome anyone able to provide a link to a paper or textbook that contradicts my sentence):     
Below are three images of measuring tapes:
With a larger unit length, a greater atom, we measure less 'space': it is the past.
With a smaller unit length, a smaller atom, we measure more space: it is the present.
Thus, quite naturally, the measure of the space expansion can point to a shrinking atom instead of the space expansion. Obviously this phenomenon can not be measure in the lab, and there is not a simple way to distinguish between the two descriptions.  
To those that mention the metric (GR) as a cause I can ask: is it a cause or a description?  GR was 'invented'  by Einstein  well before the space expansion hypotheses and he did not predicted any space expansion.     
My description is appealing to your intuition, just 'wording', such that anyone without formal training can interpret correctly what I'm saying.  
To those that have the skill and will to read a formal document, can certainly find it. 
larger unit length in the past  
 
 

smaller unit length in the present  
