I don't think Peterson is lying, he just doesn't understand Postmodernism. He hasn't read any of the texts beyond Jung.

I think in recent years he has gained a better understanding of Postmodern concepts in his various discussions with people. Instead of calling these people 'Social Marxists', I think he started calling them the correct term which is 'neo-marxists' by way of the Frankfort school. This is the basis of 'critical theory' that conservatives are calling 'woke'.

But I agree he clearly doesn't understand what he is talking about and is not inquisitive enough to learn.

I talk about how Peterson doesn't even understand modern/postmodern concepts of reality in my article here: https://medium.com/@jaime-roberts/jordan-peterson-what-is-reality-de9ae69d9d9c