Even as a supporter I can totally understand people's hesitation about jumping on board with Peterson. If you only skim his ideas with a skeptical eye you can easily get the impression that a lot of what he says is either trivially true or convoluted nonsense. His association with so many alt-right figureheads has been less than flattering, though supposedly this is a product of him agreeing to speak with anyone who wants to speak with him. Figures of the left are open to do the same.
If you dig deeper into his work, there is a lot of foundation behind all the notions he's been expressing over the last year, though it's broadly sourced. Some of it starts at a more deeply scientific level, with evolutionary biology and neurophysiology, and then psychology builds on top of that, and then politics builds on top of that. From what I've read he's tried to be earnest in his recruitment of facts from all these different domains. He certainly has the training and expertise that would let him separate the wheat from the chaffe, although sometimes he seems overly sympathetic to some of the less verifiable ideas (specific passages from Jung, for example). Even given that weakness, he's not obligated to speak in absolutely scientific terms 100% of the time. Figuring life out is ultimately more of an artistic endeavor imo.
I'd like to see more criticism come from A. people who have more specialized expertise in the domains he pulls facts from, who can debate the merits of those, or B. people who understand the risks of theoretical stacking (ie. using biology to explain psychology or politics) and can pick apart the edifice he's built as a whole. And I'd like to see these critics not be fucking dishonest hacks, at least once.
He's clearly open to this sort of discussion. He's said plenty of times that he could be wrong, and that people didn't really know what to do with his big "Maps of Meaning" book after it was published. That isn't a gauruntee of its veracity or its shortcomings - in his lectures he talks about a bunch of major books that came off the presses without much fanfare before the relevant community figured out the usefulness of them. These things can take time to digest. Based on popularity alone, his work certainly does seem useful so far.
It sucks that so few people are able to talk about this phenomenon with proper intellectual sincerity. Today's politics are toxic.