That's just not true. There are many kinds of social relations, dominance being just one particularity nasty one. Other apes also exhibit a whole range of social relations. It doesn't have to be a dog eat dog world out there, and most of the time it actually isn't.
Absolutely, and there are many kinds of social interactions at school besides bullying. My point was only that "bullying" is an expression of normal hierarchy negotiation/construction in children and should be treated as such.