There's a few different schools of thought, actually: femininity defined as "that which isn't masculine," masculine defined as "that which isn't feminine," and masculinity and femininity both defined in opposition to each other. I don't quite know which I believe yet, but... yeah, that was sloppy speaking.
The schadenfreude and sadism thing... well, I'll just say that in any society where "feminine" is defined as "weak and peaceful" and masculine is defined as "fighting things," proving your femininity will remain strongly related to sandwich abilities and proving masculinity will continue to be related to beating people up and molesting them. I mean, schadenfreude and sadism are surely not only male pursuits, but in general they are not related to "feminine" behavior, and they are not rewarded in females as they (often) are in men. So, in a sense: yes, those things
are intimately related to sexism and this entire messed-up social structure.
Furthermore, women bullying women results in an increased rank for the woman, and thus is often punished by both the female group (through the principle of "crab bucket") and the male dominant group (because it's not good to have someone threatening the upper structure). Male bullying is just dudes fighting within the power structure, and considered normal in dominance. Then, if you've got a gay guy, they can tend to be rejected by both women and men, because men are kicking out the dangerous "feminine" element to prove their dominance over feminine traits, and women are uncomfortable dealing with what is still seen as a member of the "oppressor" class.
Well, anyway... I guess this is just me being weird again, and I can send out the PM at some point (hopefully in the near future).
men get away with abuse of women except in front of other men
You're a bigger dude if you can maintain power without gaining it by beating the shit out of a woman. It's like "Look, I'm better than you--I don't even have to beat the crap out of her to prove that I'm dominant!" Kind of like the "be the bigger man and apologize" thing.
men get away with abuse of men lower on the social ladder
You need to abuse other men to gain more power within the male social structure itself.
women get away with abuse of men almost whenever they want.
What kind of man are you if you can't take someone weaker trying to usurp you? Man, you'd better be made of stronger stuff than that. You're stronger if that stuff doesn't faze you.
And women abuse each other plenty too but that's something I hardly understand at all.
Easy. The primary way to gain power is to align yourself with men. First way to align yourself with men? Abuse women. So you get plenty of women abusing women in an attempt to gain male social power. Not that it works, hoho.