> he mostly wins arguments by carefully crafting his phrases and forcing his view to less skilled communicators
I think it's the other way round. When people interview Jordan Peterson, they use pre-prepared phrases to and ascribe to him opinions and views he doesn't hold. e.g. the infamous Cathy Newman interview, "So what you're saying is".
This doesn't always happen e.g. the debate between Russell Brand and Jordan Peterson.
I don't think there would have been nearly such a controversy around his work, if he had not touched on the pronoun issue, which was about compelled speech, not even particularly about pronouns.
However that issue is a bit of a hornet's nest, and Peterson is by no means alone for being targeted, as also seen in the UK with Professor Kathleen Stock.