Why are basic physics problems neglecting to include atmospheric pressure? The value of atmospheric pressure is 101325 Pascal, which is a large value which implies the force exerted by atmosphere is 101325 N m$^{-2}$. Surely this can not be neglected, so why is atmospheric pressure neglected almost all the time in introductory physics?
 A: The atmospheric pressure is quite large, but it is also about the same everywhere. For example, if you hang a tire swing from a tree, there is atmospheric pressure on it from below, above, left right, front, and back. However, the atmospheric pressure is pretty much the same from all these directions and so there is little net force on the tire and the rope has to support almost the entire weight.
There is a small buoyant force from the atmospheric pressure; this makes the tension in the rope holding up the swing a bit smaller than it would be without the atmosphere.
Also, if you reduce the pressure inside an airtight container, you'll be able to see dramatic effects of atmospheric pressure. A classic demonstration involves boiling a small amount of water in the bottom of an aluminum soda can, then turning the can upside-down in cold water. The water vapor in the can condenses, reducing the pressure in the can, and the atmospheric pressure outside the can quickly crushes it. The can doesn't crush under ordinary circumstances, though, because the atmospheric pressure on the inside is the same as the pressure on the outside.
So we could take atmospheric pressure into account in every calculation, but usually it does not result in a large net force on objects of interest because it's about the same everywhere. You're right that atmospheric pressure is strong, though, so when it isn't roughly balanced everywhere it can have dramatic effects.
You will also need to account for atmospheric pressure when doing thermodynamics, for example finding the boiling point of water.
A: Short Answer
Adding in that effect does not alter the answer that much or is too hard.
Longer Answer
Real-world conditions are ignored for several reasons:

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*The inclusion of that effect does not alter the answer that much, and most students (or instruments) may not be able to calculate the effect of it since it's so small. If the effect is immeasurably small, then why bother?

*The required effort and math to model those affects are not in reach of the student. This is why introductory physics problems often happen in space, or in a vacuum, or on frictionless surfaces.

*The effects of real-world conditions is not the point of the class. As in so many things, baby steps come first. For instance, if one does not understand forces, adding in more forces to a problem will not help them. It will only confuse and be a negative experience overall.

Approximations and Why We Can Ignore Them

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*Atmospheric Pressure: much like the acceleration due to gravity, atmospheric pressure doesn't actually change the outcome of most problems because the pressure on the top of an object is really close to the pressure on the bottom. If the pressure difference is significant (like in an inflated tire or balloon), this effect is included. One should also note that pressure difference is when pressure generally matters, not absolute pressure.

*Acceleration due to Gravity on Earth: technically this value changes with height, so every time a slight variation in height occurs, you should have a new value. On the surface of the earth and concerning most everyday objects, this change in value is REALLY SMALL so it's ignored.

*Friction: friction is often excluded because it's not the point of the homework or lecture. A professor or teacher is busy explaining a different concept, and they don't want to confuse their students. Sometimes, and in special circumstances, it can be neglected when doing "real" physics/engineering. In some cases, like with air resistance, the students do not have the math/models required to accurately account for it.

A: Because physics problems are usually abstracted idealizations that only approximate real world conditions. When real conditions have to be taken into account it is called "engineering". Otherwise it's the apocryphal spherical horse moving in a vacuum...
