When you are flying in an airplane why can't you see other airplanes?

You can, if you know where and when to look. Generally aviation rules enforce a minimum separation between aircraft on the same flight level.

Generally the separation (controlled airspace) for aircraft flying the same direction at the same level is 5 nautical miles (9.3 km). That distance means that the other aircraft will be hard to see (appears like a small dot).

Often when flying you do see other aircraft crossing at + or - 1000 feet....

If you can see another aircraft at the same level, this is not generally a good thing...

Under visual flight rules, planes must only remain well clear of each other, so you may see another aeroplane if you are in a small plane flying outside of Controlled areas.. your pilot's prime job is to see these planes and avoid them.