Peterson came to public attention because he refused to use politically correct gender pronouns; and I think that is key to understanding who he is, and why he's so popular. He refused to be bullied by political correctness extremists.
Remember the Cathy Newman interview on Channel 4. I have no wish to demonise Cathy Newman, but in typical news media style, it was a gotcha interview, wherein Peterson was bombarded with gotcha questions, and he refused to be intimidated and answered those questions. I think they got into it over the supposed gender pay gap.
Then, far lefty keyboard warriors like Kenosha Kid - take those examples out of context and claim this typifies Peterson's message, but it doesn't. This quote:
"...it’s so whiny, it’s just enough to drive a modern person mad to listen to these suburban housewives from the late ’50s ensconced in their comfortable secure lives complaining about the fact that they’re bored because they don’t have enough opportunity. It’s like, Jesus get a hobby. For Christ’s sake."
....is so endlessly reproduced out of context by craven left wing bullies citing other craven left wing bullies, the original context doesn't appear in a google search.
Forced monogamy is not something Peterson advocates as government policy. Rather he identifies it as the response of nature and civilisation to the monopolization of sexual opportunity by alpha males, and a violent competition for hierarchy. It's nothing that Claude Levi Strauss hasn't said in discussing the kinship relations of hunter gather societies. This is from Peterson himself:
"My motivated critics couldn’t contain their joyful glee this week at discovering my hypothetical support for a Handmaid’s Tale-type patriarchal social structure as (let’s say) hinted at in Nellie Bowles’ New York Times article presenting her take on my ideas.
It’s been a truism among anthropologists and biologically-oriented psychologists for decades that all human societies face two primary tasks: regulation of female reproduction (so the babies don’t die, you see) and male aggression (so that everyone doesn’t die). The social enforcement of monogamy happens to be an effective means of addressing both issues, as most societies have come to realize (pair-bonded marriages constituting, as they do, a human universal (see the list of human universals here, derived from Donald Brown’s book by that name)."
https://www.jordanbpeterson.com/media/on-the-new-york-times-and-enforced-monogamy/
The problem with politically correct lefty keyboard warriors; apart from their overwhelming ignorance, is their overwhelming ignorance of the implications for society - of their supposed moral goods.