I've never agreed with Peterson much, and this article was really eye opening. I think the expression "not even wrong" precisely nails it: he talks in such broad strokes and general terms that you cannot even start a debate before he swamps you with more generalizations.
The problem is, as OP experienced, that Peterson (although he would never admit as much) and his followers use this rhetoric to justify misogynistic, racist, sexist, and other "traditionalist" views, that are a real danger to the people on the receiving end.
I just had this with a user on here. Dude just went off the deep end with all this nonsense I couldn't even begin to respond without dedicating the day to unwrapping his tangents. I made his note "a little silly goose" and moved on.
It's the only thing you can do. Some of these people have given up on reality and live in a really weird alt right bubble, so entrenched it's impossible for them to leave. Don't bother with 'em, waste of time, Block And Move On, or BAMO for short. Works every time!