Peterson is, above all, logical. In any argument he makes - he demonstrates the logic and causality.
He then demonstrates the illogic, contradictions (and usually the utter stupidity) of the ideas he is attacking.
Its how every talk he gives proceeds.
Post-modern emotionalism and nihilism always get exposed badly, and the left doesn’t like it, so they are trying to shut him up
The 'left' is the emptiness - one of many reasons the left is trying to shut him up...