You do realize that your three rules are all things that Peterson does in spades, right?

1. He calls people he disagress with names like “crazy harpie” and “clueless religious.”
2. He is rampantly hypocritical, e.g., MLK had a duty to his culture even though his “house” was not in order, but no one else should do that. Hierarchy is good because it’s natural but monogamy should be socially enforced because it’s what is best for society (even though it isn’t natural — or it wouldn’t need to be enforced).
3. He quite frequently rants emotionally about all kinds of things (see #1) and even admits that he has a short fuse and can get carried away. Perhaps all of this is just a further manifestion of failing with rule #2……. or just evidence of what you suggested it means — narcissism and pride.

The cards are there on the table. I’m just calling ‘em.