My problem with Peterson is twofold. First, his whole philosophy rests on the naturalistic fallacy (remember the infamous lobster argument in defense of inequality?). And second, his argument style is all motte-bailey. Ie he makes a claim that’s ambiguous and potentially very extreme, and then when challenged on it falls back to a far less controversial (but also less interesting) interpretation of what he said to cast his critics as the extreme ones.
In other words, I find him sloppy and dishonest, and all his protestations to the contrary - that he chooses his words very carefully - he utters because on some level he is aware of his own incoherence.