The book I meant is that one.
Its basic framing is between struggle and chaos, and Peterson names chaos as the eternally feminine and order as the eternally masculine, and then mines various religions for support of that while mostly erasing the female goddesses and ideas which don't fit into that framework.
Although he wants us to tiptoe along the borderline of order and chaos, it is very clear that he also believes the old Western sex-based hierarchies are the correct and natural ones, i.e., men above women, and that any attempt to get rid of them results in chaos as in Mao's China.
Chapter 11 in the book is about education and the short-changing of boys in it. He asserts, in that chapter, that the reason for the rise of the far-right in Europe and the election of Donald Trump is the feminisation of the culture.
Peterson then goes on to present most of the conservative arguments about why having so many women in higher education is, in fact, bad for women, mostly based on the argument that women with higher education levels will not find a man to marry or if they do, the marriage will be unhappy. Data on that shows pretty much the opposite, i.e., women with university education, at least in the US, are more likely to be married and to stay married than women with much less education.
He also presents a novel theory about why adolescent males might not want to go to college:
He believes that any 'game' in which boys play against girls or men against women cannot be won by the boys or men, so they will refuse to play that game. According to him, if girls win in such a game, they are praised, and if they lose, that is seen as understandable, while if boys win in such a game this is not seen as OK and for him to lose is even less OK.
And that's why adolescent boys won't go to college if college is viewed as a girls' intellectual game, says Petersen.
But this whole theory is based on the assumed inferiority of women and girls, to begin with! That is the reason why boys or men winning is deemed as not really winning, and that is the reason why boys or men losing is seen as particularly bad.
And so on.
I find him an interesting writer in places, perhaps too pessimistic and dark in some ways, and but I also find him rather clearly opposed to feminism of any kind.