Yeah, there is a bewildering array of animal social proclivities, sexual strategies and behaviors, tendencies towards hierarchy, and so on. He could, at minimum, have chosen a more social animal to make his point - but in general he shouldn't really be drawing from other animals (or at least non-primate animals) at all, because there is so much diversity that any choice will say more about him than about the point he's trying to make.
Humans have an extremely high level of social interaction, fairly low but certainly nonzero sexual dimorphism, strong pair bonding with male parental involvement in raising children, a relatively low level of hierarchy in hunter-gatherer societies but a much greater tendency towards hierarchy in more complex societies, and a level of violence that varies enormously from culture to culture. Offhand, I can't think of what the best animal analogue to us would be. But I do know that finding a better one wouldn't prove much.
People who discuss things with Peterson need to dissect some of his talking points to show that reality is more complex than he is making it appear.
One thing that he will admit is that inequality, if taken to extremes, causes severe social dysfunction. Rather than arguing for equality among race/gender/sexuality lines and allowing him to strawman them as a "postmodern neo-Marxist", someone arguing with him should simply promote social democracy. Say that you don't think that everyone should have exactly equal outcomes, but given the tendency of income to distribute along a very skewed Pareto distribution, and the high stability and social cohesion of societies with Gini coefficients of c. 0.20, we should aim for that through progressive taxation and active redistribution with a strong safety net. The successful can still be substantially better-off than average, just not in the winner-take-all way we see in the US, and increasingly in Canada and the UK.
I haven't actually seen someone engage him along social democratic lines. Almost nobody is arguing for his "perfect equality of outcome" strawman anyway, yet I haven't seen anyone call him on it.