I wonder if the work of Alice Miller might not be relevant here, especially WRT the tendency of those in power to side with the bullies, and also WRT the endemic nature of bullying in our culture. The truisms about cycles of violence and people learning abusive behavior from their abusive home lives don’t go far enough. Like ginmar says, there’s no epidemic of abused women taking out their frustrations on weaker targets. (I imagine that if there were, we’d be hearing all about it, what with the international repository for hypocritical misogyny that is the mass media). But I think that, for people to change from being the victims of abuse to being its perpetrators, some additional steps need to be taken. Somehow, you have to distance yourself from victimhood, whether by identifying with your abuser ("It made me stronger/taught me to be a man," that sort of thing), forgetting what it was really like ("Just ignore it and it will go away") or blaming the victim ("You must have done something to provoke them/Why didn’t you stand up for yourself?").
Some commenters tried to anchor bullying (and the encouragement of bullying by the adults who are supposed to be stopping it) in humanity's primate roots. While there is probably something to that (primates are highly social animals, with complex dominance hierarchies), I also think much of it is cultural. Humans differ from chimpanzees in the extent to which we learn by imitation, which may explain the greater degree of cultural sophistication we have attained. But this very faculty for imitation and social learning probably also contributes to our brutal treatment of nonconformists.
No, I think the motivations we are looking for aren't primarily evolutionary at all, but cultural. We live in a profoundly unequal society, with clear "winners" and "losers," and in which the governing philosophy of one of the two major parties is that merely being a "winner" is a sign of moral and social worth, and serves as its own justification for everything you do to become one. Furthermore, because we are apes, and are therefore more tribal than rational, our workplaces and political power structures are often organized around social ties rather than objective merit. Few people actively stand against bullies because so many of us identify with them. Either we are them in different contexts, or we wish we could be them.
By contrast, very few people want to identify with the victim. Adults might minimize the damage of what they're experiencing (claiming everyone is bullied, it's no big deal, and "When I was your age, I learned to fight back!"-style victim-blaming), or deliver a patently insincere speech on the virtues of nonviolently ignoring the bully (which serves to isolate the victim by portraying the speechifying adult as somehow above the entire question of bullying). In the first instance, the adult is identifying with the bully by claiming that bullying is either a good thing or unavoidable, and the victim is wrong for failing to deal with it. Even in the second instance, where bullying is at least assumed to be a bad thing, the adult distances himself or herself from the victim by erecting a sort of wall of sanctimony between them. The adult who clings to such obvious platitudes is clearly one who has never had to deal with these issues in his or her own life! I think a great deal of our society's refusal to deal with the problem of bullying on a large scale derives from our collective unwillingness to acknowledge our own (or our children's) victimhood. In an unequal society, one of the most demoralizing thoughts that can strike a person is the thought that they might not be one of the "winners."