The fact that humans were cooperative and relatively egalitarian for millions of formative years in the Stone Age certainly throws a mighty monkey wrench into Peterson's social Darwinian narrative.
It's clear why humans would be cooperative and social, because we have to work together to care for our babies which are born more helpless than the offspring of some other species.
But we're also more sensitive to cultural distinctions. It took millions of years for Stone Age human brains to work this out and to become behaviourally modern, but eventually they did so and this was likely another source of social inequality.
In our nomadic condition, cultural inequalities couldn't be pursued or enforced, because wealth couldn't be hoarded. But sedentary societies provided the opportunity for culture to metastasize. Suddenly there were gods to be appeased, and a priestly class to act on behalf of the spirits that could be accessed only in the coveted temples.
I think the upshot is that the human brain is at war with itself on multiple fronts. We may still have primitive instincts to form dominance hierarchies or to recognize the efficiency of the law of oligarchy. We also have a social instinct, and we're drawn to a symbolic, cultural realm which can reify these instincts and provide excuses for great heroism and for egregious injustices.