The emphasis here on Peterson's gender traditionalism gets to the heart of why so many people call Peterson a "fascist" — his concern over emasculation, "enforced monogamy" and terrible chaotic femininity. nytimes.com/2018/05/18/sty…
In 1977, Klaus Theweleit published "Male Fantasies" a psychological study of fascism by looking at the Freikorps, the earliest post-war male reactionaries. Theweleit noticed that Freikorpsmen bifurcated the women they encountered into two camps. The "white" and the "red."
The "red women," Theweleit observed, were the unruly communist women — sexually liberated, disorderly, politically brash, bloody, effusive. Bacchic. Here are two characterizations of his findings, via @Awl and @Timeline_Now : 
This is Peterson's characterization of what he calls the modern woman's "harpy sister," the progressive women activists who are "undermining the masculine power of the culture" in a way he sees as "fatal."
Many people rightfully take note of his lamenting that violence is unavailable as a regulating force against ungovernable women. But don't miss the notion of fatality — that the feminine overrun of patriarchy is some sort of suicidal ideation of Western culture.
You see the Suicide-of-the-West rhetoric tethered to race when it comes to American reactionaries, like in Tucker Carlson's recent TV segments about how liberalism is bringing in immigrants who are undermining male birth rates.
But if you want more pure political men's reaction tied to suicidal ideation and anti-liberalism, the French have been innovating for decades. Michel Houellebecq, Eric Zemmour. This is ill-suited to tweets though, I should probably just write this.
Anyway, it's worth remembering that Peterson invokes the quiet threat of violence fairly often. His critique of trans activism, of feminism, of white privilege rhetoric isn't just that it's undermining masculinity, but that it's totalitarian, and that it could get us all killed.
Lastly: To pull a Jordan Peterson here, I'm not necessarily saying "Jordan Peterson is a fascist." I am saying that Jordan Peterson's rhetoric around gender has uniquely strong echoes of men's reactionary thought going back a century. He is part of a tradition.
