Thank you!

The phrase "push papers" implies that the paperwork that one does is not very important. "My friend works in an office" or "My friend is a secretary" is polite. "My friend pushes papers in an office" sounds like you're saying your friend's work is not important.

Pushing papers is another way to say you did an office job or you were a secretary. You maybe took notes, you filed papers, you worked at a desk. That would be the opposite of what you would expect to do in the military, where you might fight a battle, shoot a gun, fly a plane, etc. So pushing papers while in the military means you didn't do any work that you would expect but instead you worked in an office type job.