Peterson is a rising star in the 'Men's Rights' movement and a frequently quoted crank. He rose to fame in part after refusing to acknowledge transgender students.
Among his many weird prescriptions is the idea that human social order should aspire to that of lobsters. No thanks. Cultural critics generally are not trained evolutionary biologists.
In her long, thoughtful -- and ultimately devastating -- Times Literary Supplement critique of Peterson's book, Kate Mann tries to evaluate Peterson on his own terms, taking his arguments seriously enough to engage with, and having engaged with them, reveals their flimsiness, laziness and the convenient elisions and omissions they rely on.
For those looking for more context on the (largely North America-centric "Men's Rights" sub culture I highly recommend "We Hunted The Mammoth" blog. http://www.wehuntedthemammoth.com/faq/
Postscript: well, that was fast.