Everyone makes the retarded argument "ermagerd, lobsters diverged from us a long time ago, that makes it retarded" that's the point, the point is to show that it's not a cultural phenomenon, but a biological one so deep that it manifests across species as different as humans and lobsters.
And yes, Jordan Peterson does in the broad span of his work cite to creatures we are more closely related to, such as when referring to experiments on rats, or the social structures of other primates. He does mention them as well. Everyone just likes to hone in on the misconception that he only talks about the lobster.
It's also a complete mischaracterization of him to suggest that he's saying people shouldn't cooperate. Because he does mention closer relatives such as primates, and when discussing their social structures he mentions that things tend to not turn out so well for the alpha chimps that aren't cooperative or reciprocal in their relationship with the other chimps.
He has also stated that a reasonable political left-wing is a necessary part of political discourse, because in his view just as the existence of competence hierarchies is necessary in the pursuit of something of value which the right recognizes, the left is also necessary because people are also displaced and left at the bottom in unfortunate positions, and that it's not a good thing to have people stack up at the bottom in need because then they're suffering as individuals and it destabilizes society as a whole. He has actually praised some of the historic accomplishments of the political left in Canada such as workers protections, the Canadian healthcare system, etc. and think it's a good thing for part of the political system to advocate for the working class.
He also has said for people to adopt responsibility not just for selfish ambition but so they can be of use to the people around them. Something he said was that it's an admirable goal to be the kind of person the rest of your family can rely on at a funeral when a loved one dies. He argues that the point of personal responsibility isn't just so that you can take care of yourself but also your family and the broader community.
You seem to have this misguided understanding of Jordan Peterson's views that essentially amounts to a caricature. He's not some proponent of the idea that cooperation is bad and that it should just be every man for himself, and has said many such things to the contrary.