do you point your eyes down when you want to look up?
If you were controlling their movement manually from behind them (analogous to manually moving a stick to change visual focus of a camera in front of it), then yes, you would pull down on them to make the eye look upward, like you do for television cameras.
You would also need to invert the x-axis if you follow that reasoning, but so many people dont, so this reasoning doesnt hold up. Fact is inverted use is pretty much entirely arbitrary, people just stuck with whatever they got used to first and they could just as easily learn any other scheme with a little bit of time and use
It is certainly interesting. Sometimes I do use inverted X for camera in some games, but yeah generally I only invert Y axis for FPS, and the logic should be the same for the X axis but it isn't.
It's funny though how serious people take this, I was taking shit from my friends the other day when we were playing CoD and they kept having to change the invert every match when I handed them the controller, they both prefer non inverted and were like what's wrong with you you use the wrong scheme, THIS ISN'T THE DEFAULT YOU ARE WRONG lol