There are generalized definitions of a pencil pusher being someone with a meaningless job, specific to military service however, a Pencil Pusher is most often times someone who fucked up in such a way they can no longer be trusted to do anything of value. These people usually have some sort of assault charge pending and are holding over for paperwork so they are given some moronic tasking to fill their time and keep up appearances. They are also more comment then not, officers, as the enlisted component would like face chapter up front. These individuals are commonly hated for an array of reasons but usually revolve around the actions that got them there.
specialist: what's LT smith doing in the yard?
corporal: man he finally got caught
specialist: no way I thought it was just a rumor
corporal: might have started there but DNA dont lie
specialist: so he really did it?
corporal: ya he raped that girl in TRADOC
A concept, idea, project, etc. that is so confusing, it leads the habitual pencilbiter to skip biting the unfortunate number two, and go straight to eating it.
"Hey, y'know this question's a real pencil-eater, it's been stumping me for weeks!"
"This project's such a pencil-eater, you mean to tell me I need how many sources for it? I can't even find one! Who wrote this textbook anyway?!"
"Man, adobe choosing to trick its customers into a year long subscription sure is a real pencil-eater! It's like they wanted a lawsuit or something!"