Arnold Kling has a few reasons for being less than fully bought into Jordan Peterson:
He is a spellbinding speaker but his first book, Maps of Meaning, was turgid. There is something disconcerting about the fact that his ideas seem to come across better in a format that allows for less editorial polishing. I noted this in December of 2016, when the Peterson tsunami was just forming.
Some of his ideas are mystical and sound really strange.
He gains some of his stature by attacking post-modernists who are intellectual weak, at least in the way that he presents them. For me, it is more impressive to take on stronger opponents than weaker ones.
He may now be over-rated by his fans on the right. But he is badly, badly, under-rated by smug leftists whose ability to understand opposing viewpoints pales in comparison with his.
Using the three-axes model, I put Peterson firmly in the conservative camp. He sees civilization as fragile and precious, and he is animated by the civilization vs. barbarism axis.