Here, for example, Peterson questions the radical left's gender ideology, citing its utter lack of objectivity. If the scientific evidence is presented to me, I can accept that a very small number of people have disorders of gender identity that are best treated through medical transition. But trans activists aren't interested in evidence or in careful diagnosis; they just want to force other people to turn off their skepticism and grant self-declared trans folks unearned power and moral standing. Like Peterson, I'm not down with that.
Here, Peterson avers that unfettered free speech is vital because free speech is how we think. I understand and appreciate this argument on a gut level because I grew up with a father who regularly encouraged me to say whatever was on my mind so that he could play devil's advocate and tear me down. At the time, it drove me crazy -- but as an adult, I now recognize how brilliant a teacher Dad actually was. We reason better when we're not endlessly affirmed in our beliefs; we have to butt up against people with whom we disagree or else we'll lose the ability to articulate, defend, and - when necessary - correct our worldviews. Plus, as Peterson points out, driving certain speech underground because it is "hateful" or whatever doesn't actually cure bigotry. No: Suppression of "hate speech" enhances its allure. If suppression of "hate speech" actually worked, Trump would not be president. Alas, "build a wall" is now a motto of the new punk.
This video is longer, but it's also worth a listen. I actually cheer when Peterson declares that flying flags emblazoned with the hammer and sickle is tantamount to waving flags emblazoned with the swastika. Because yeah: Compared to the communists, Hitler was just a piker.
Oh, and if you're interested in academic psychology at all, I also highly recommend visiting Peterson's personal YouTube channel, which is loaded with free lectures on the science of personality and ideological formation. Go and watch!