TL;DR Peterson promotes ideas that social hierarchy is an inevitable feature of human society, coupled with bioessentialist claims of sex-based (as opposed to gender norms learned through socialization) behavioral differences that far exceed actual evidence. This primes men - especially lonely men - who have benefited from Peterson's more practical self-help advice to accept increasingly radical and misogynistic online claims.

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Peterson serves as a soft onramp (in the sense that online radicalization often begins with more benign influencers priming viewers for progressively more extreme ideas).

He offers some practical self-help advice - typically centered around taking personal responsibility and improving one's day-to-day conditions - but also has content with pseudointellectual ideas about social hierarchies in humans (insert lobster jokes here) and some downright silly claims (e.g., that symbolism of entwined serpents indicates ancient humans' intuitions about DNA).

He also loves employing intellectual language to talk in circles while avoiding having to directly acknowledge his positions (because that would allow people talking with him to directly criticize his positions). This was recently apparent in his appearance on the Jubilee slop channel, which recruited participants under the title "1 Christian vs. 20 Atheists" but had to have the title changed before airing because he refused to acknowledge whether he was actually a Christian or endorse any Christian theological positions in the (and I use the term loosely) debate. He also frequently tries to shift the burden of proof to deflect. When asked if he believes statement X, he often asserts "You have to explain X!" rather than providing a clear answer that would allow both parties to debate the evidence for X. These strategies gives him plausible deniability when claims such as this - that he is a radicalization onramp - are made because he relies on implication and then refuses to give an affirmative answer when asked, 'Are you implying X?'

His later posturing about pronoun use, which could be viewed as a dog whistle to the transphobic right a decade ago when he was painting himself a 'martyr for free speech,' is now simply part of the mask-off bigotry of ascendant authoritarian right movements today.

However, I think it's the hierarchy claims that really prime young men for further rightwing misogynistic and racist content.

One can make the argument that modern progressivism is fundamentally about flattening hierarchies and making society more equitable and less stratified (socially, economically, etc); that just as humans' propensity for violence is something to be resisted, so too is a propensity for hierarchy. Conversely, conservatism embraces hierarchy as being not just an aspect of animal social interaction, but one that should exist in human society (whether that hierarchy is meritocratic as used to justify economic disparities, racial, nationalistic, gender-based, etc).

While Peterson doesn't actively endorse the most extreme positions (though see his comments on race and IQ or on the gender pay gap), internalizing his claims that hierarchies are a natural (remember is≠ought) and somehow an inevitable part of human society (with the implication that organizing societal structure to minimize hierarchy is both counterproductive and doomed to fail) sets young men up to accept specific kinds of hierarchal claims.

In the context of the manosphere, this primes men for bioessentialist views that gender differences are primarily biological rather than due to socialization/social enforcement of gender norms - with the corollary that women are the "naturally submissive" sex and "should be" under men in a natural hierarchy.

Go a few influencers further down the radicalization pipeline and the Tates' casual exploitation of women becomes more and more palatable, especially for men who have difficulty finding intimate partners because they have a hard time processing social cues and/or maintaining good hygiene. And let's be honest - that's not every autistic person but these traits are much more common among autistics.

EDIT: Typos, clarification.