There is an inescapable human nature which means that we have no choice but to be organized hierarchically. We have evolved but we are no different from lobsters in our predilection for hierarchy and that is our fate as a species in spite of evidence to the contrary (which is all bogus). Our only choice is to find ways of ameliorating the worst effects (but JP seems to say little about that and in fact condemns outright people's efforts to do so). Women tend to be more agreeable by nature than men because they have to accommodate infants (1), while men are more competitive. Liberal philosophies that flout inescapable human nature and blame Western patriarchy for gender inequality are out to lunch and very dangerous - especially "post-modern Marxism" (PMM) which is actually a position of totalitarian Maoism in that proponents group people under banners of identity politics. (Well, Derrida, so much for difference!) Proponents of PMM are dangerous not only because they harbour insidious authoritarian and totalitarian tendencies but because their actions will cause a backlash among men and give rise to cultural manifestations of the dark side of masculinity.2 It's best that we stick to what nature intended for us in order to prevent or minimize this impending catastrophe.
Nature and culture are of course inextricable. As Merlin Donald points out, no human would be able to achieve anything like human cognitive potential without being imbedded in culture, which is where both the ancestry of our ideas and abilities, and the seeds of our potential, repose. Human cognition evolves with culture, and cultural evolution since prehistoric times is largely driven by technological advancements, especially in communicating through stories, writing, and other modes of external memory storage.
It turns out that technological advancements also not surprisingly influence the organization of human societies and the focus of institutions. Any socio-political arrangement is how people organize themselves to produce and distribute what they need and want given a certain level of technology. Ian Morris explores the prehistory and history of social organization and power relations between nations in his book, Why the West Rules for Now.
Consider, then, the social role of women in relation to the work they do either in or out of the home in relation to technology. Women used to produce manually much of what was used in the household. With modern manufacturing, mass production, the availability and continuous improvement of the efficiency of household appliances and the invention of the pill, much of women's work in the home became unnecessary. Over time, the nature of work and our political and legal institutions have changed to reflect the fact that most of women's traditional work is not now needed in the home. There's usually an awkward or very uncomfortable lag between technical change and the reconfiguration of society that follows it.
The story of what a woman or man is in society has changed over millennia, is changing and will continue to change. During the last few centuries, the narrative that human beings have used to explain gender roles has been articulated and sustained by those who dominated in the public sphere - i.e., men of power and influence. We are currently in a lag period between the changed technology and the story that is going to make sense of it (and still finding out who will most benefit from that story).
What's thrown us for a loop is that the technology is changing so fast that automation threatens to undermine our entire system of economic arrangements based on wage labour. Most jobs will become unnecessary, so ask yourself, how is the wealth going to be redistributed? Meanwhile the underclass of unemployable people is becoming larger and feeling their loss of power ever more acutely. This is especially so for men, who at least had enjoyed an advantage of higher social status than women in the same economic bracket. These are the people who I expect tend to vote in strong man politicians and fall victim to false nostalgia. There is a backlash and the darkness looms, but it has to do not with PMMs but with the sense that, historically, men have had rights over women; their sense of threat and humiliation that women, who were formerly accorded lower social status, are now getting small gains in social status by becoming more involved in the public (versus the private) sphere. (In some societies, women are not even supposed to have a public face.) Things are changing too fast for the narrative to catch up and people are stressed out. During uncertain or fearful times, people's views tend to become more conservative. People retrench.
Chimamanda Adichie says that we do girls a great disservice by raising them to accommodate men's egos. This unpleasant obligation is embedded in the narrative that all of us have inherited in one variant or another. In some societies women are still blamed for men's inability to master their sexual impulses. The tendency for women to be agreeable and accommodating is an effect of inequality, not a cause. Being agreeable and accommodating is different from being loving and kind, caring and considerate. It is a defence. It becomes a defence that fosters resentment of their own capacity for caring and it makes those without the "right balance" of agreeableness and commitedness into scapegoats. "The beast" of the masculine feared by Peterson is one that he generously sustains with circular rationalizations.
because they'll do everything they won't
. “If men are pushed too hard to feminize,” he warns, “they will become more and more interested in harsh, fascist political ideology.” https://www.newyorker.com/magazine/2018/03/05/jordan-petersons-gospel-of-masculinity (More likely, men are being marginalized by increasingly flat wages or unemployment, and humiliated they scapegoat, as explained above.)