Yeah, bullying typically involves social elevation and ego boosting. It is a psychological thing. If you can belittle them in the process, you can ruin their motivation for what they're doing.
On the other hand, this really depends on the situation, because quite frankly many bullies are blitheringly stupid to the point that they use it as a shield. You come up with some clever insult or put down in front of others and they can shrug it off as "LOL you use big words dood, I don't understand you. Quite reading so many damn books." Crowd laughs and they're free to frame the conflict as purely physical. I've met this obstacle plenty of times, and it was in a culture that frowned heavily on any kind of bookishness. They could carry their stupidity openly like a banner and it wouldn't hinder them at all.
And if the bully is more socialite than thug, you're better off just ignoring them anyway.
As for the sexism issues... I don't think it's a subject that can really be explained easily. There are so many different perspectives, motivations, cultures, etc at play. I mean I agree with Vector's explanations in general on an academic level. It's easy to see how those explanations line up with instincts present in the majority of pack mammals. At the same time, we're more complex creatures than that and it's easy to frame things differently or list cases from personal experience that contradict those explanations.
One of the biggest problems with social behavior theories in general, and this is a good case of that, is they tend to undermine its own validity by being impossible to disprove. This was one of the first things my Psych 101 class made as a point of caution. It's easy to get caught up in one thought formula because of how easy it is to filter any input through, without realizing that you're conforming your data to the theory and not vice versa. This doesn't mean it's wrong, but it does call usefulness into question.
Male = Violent/Dominant
Female = Anything else
Any behavior can be easily re-framed to fit the theory without leaving room for other explanations. If a female is acting violent/dominant, they're trying to usurp male power. If a male is being violent they're just being male. If a male is being nonviolent/submissive, they're just weak/low on the social ladder and know they can't challenge their superiors. If a female is submissive, they're just being female.
I honestly hope you are not offended by and enjoy me losing my composure a little and expressing myself very frankly for a while. In two parts.
My personal experience with women is that somewhere deep down, they're incredibly vicious, even if they might not show it often. Feral, even. They're territorial and tend not to trust one another. I've never known a single female who had more than a couple female friends whom they truly trusted and considered a real friend, but they all keep massive lists of acquaintances who they keep careful tabs on and are constantly suspicious of in every way imaginable. They snipe on each other's petty differences behind their backs and play this game trying to put each other down as much as possible in secret, and then exploding into massive epic gory battles of flying hair, teeth, and nails the moment one of those secrets escapes, which was probably strategically revealed by a third party merely wishing to pit enemies against each other. They also never forgive each other for anything, ever.
And what really gets me is how they'll openly discuss these qualities with a man and admit to having them themselves and how terrible it is and put down their own gender every bit as badly as you probably think I am right now... and continue to carry on being that way. For example, I have one female co-worker who is especially bad about this stuff and has discussed her own hatred of women with me multiple times for being "sniping, petty bitches". My manager frequently sits me next to her, because I'm the most tolerant and diplomatic person he has. I watch her be nice and cheerful to female co-workers to their faces and them fume with annoyance as soon as they walk away, even if absolutely nothing noteworthy happened. I'll ask her why and she can't even explain it other than her own misogynistic paranoia and then pick on every little flaw she can think of about them and about how they're probably talking about her behind her back right now. I'll point out the hypocrisy in her attitude and she'll just laugh and shrug it off with some remark like "Yeah, it takes one to know one." Then she complains to her manager constantly about how there aren't enough women in the office and she feels alone all the time. This is a slightly extreme example, but every female I know seems to reveal themselves to be like this to some degree as soon as they trust and confide in me.
And just to balance, men aren't any better. They'll be brutish and cruel to each other one minute and the next they'll act as if it never happened and try (like honestly try) to be your friend. They'll say one thing and do another and be completely incapable of seeing the contradiction in their ways. Their own misogyny is a prime example. They're never as ferocious as when they think they're defending a female from another male, and then they'll be every bit as abusive in their own homes. And they'll mentally BSOD before they'll ever be honest with themselves about it. At least women seem to be honest with themselves, which seems to be a component of their self-hatred.
And there are exceptions on both sides. There are some men (like me) who truly don't care how far removed they are from alpha male status and either end up at the bottom social rung or choose to be as non-social as possible, and some women who aren't full of hatred for all other females but can't get along with them anyway because the rest are.
In summary, I find human social behavior in general to be incredibly hypocritical and miserable for most everyone. What really confounds me to no end is how much people are simultaneously aware and unaware of these problems and their origins. I will complain about people and get remarks like "Whatever. People are people. It is what it is." When other people complain about people, I'll try to reassure them that the entire human race isn't made of suck and discuss the origins of the problems they're complaining about... and most people will then turn around and start defending the very behaviors and causes of those behaviors that just before they were bitching about. I don't get it.
And I can understand on an academic level why people behave the way they do. My brother (the non-autistic one) studies psychology. I know two people who have worked in behavior therapy. I get frequent input from two more people who are PhDs in biology who mainly study animal behavior. I've heard every "People are X" simplified statement there is, and know all the instinctual explanations for them.
At the same time, I've been observing people, most often as an outsider, for a very long time and know that people are not always X and act on motivations all the time that are not purely instinctual. People make choices. I also know that as much as I hate people, I also love them. I've only met a few people in my entire life that I honestly didn't believe to be basically good people with positive qualities to be found if I could just get in an honest conversation with them in a private or small group setting. But then I see how they behave in daily interactions with large groups and wonder how they can be the same person.
I just don't get it. I obsess about it. My family has often told me that they wonder if I'm not autistic because of how different I am and how much trouble I have relating to normal social behaviors. I know I'm not. I don't share any of the other difficulties or qualites that autistics tend to have. But I do get the feeling often of having been 'born on the wrong planet.' I even went through a stage where I'd convinced myself I wasn't human, because I just don't understand how people can be so self-contradicting. The biggest difference I see between myself and most other people is I just cannot live without self-respect. It is the entirety of my well-being. I have to be consistent and honest with myself. I cannot say one thing and do another. Other people can. Many seem to maintain ample self-respect that they shouldn't deserve by their own criteria. Perhaps the biggest mystery to me is how people are so capable of lying to themselves when it benefits them. I can't do it. It's like some magic that everyone but me has. It allows them to hate other people when they do something they know to be wrong, and then go on to do those very same things themselves without hating themselves.
And actually I probably wouldn't be so different at all if not for the bizarre circumstances of my childhood, where I struggled to find acceptance for years in a hostile environment before running into some personal revelations that started me on the path to lunacy.
Yeah, I still have problems... just like everyone else. I feel I can at least get away with sharing them here. I might post my summarized relevant life story thing tomorrow, as some others have.
Edit:
The issue is that people make themselves a target and then don't seek to rectify the situation. You have to prove you're capable (and willing to) give 10x as hard as you take. If they insult you, you throw their clothes in the showers during "gym". If they do that to you, then you flush their's down the toilet. It'll get to the point where they realise, "Oh, shit, if I carry on I'm going to get seriously fucked up."
This basically requires being worse than the other person. I can't do this and can't bring myself to recommend it to others. 'They started it' has never been sufficient reasoning in my mind to dish out more than one takes, unless one faces death or permanent injury.