Professor Peterson is an intelligent and thoughtful academic who has found himself at the focus of attacks from the neo-Marxists that are dominating the conversation at elite universities.
If all of this is a mystery to you have a look at his channel and do some research on recent events. Free speech is under attack from Authoritarian PC activists.
I watched his video and quite frankly, I think there are bigger and more obvious democratic threats at the moment than a bunch of blue-haired kids who wish to be called "xir" in Canada.
That free speech is supposedly under threat in Canada because of the change to legislation is very much his interpretation of the relevant legal texts, and his argument that him being "silenced" (eh what? Is he not having a public debate?) because of actions of his university is very weak: It is common that universities have a stricter code of conduct than the rest of society, for instance, you can be fired or reprimanded for conduct that would not meet the legal standard of harassment.
On the other hand, on the most positive interpretation, a very sizeable portion of the US electorate is positively being trolled by organized troll news outlets and live in an information bubble where they can't take informed decisions because they believe fundamentally false things. Worse yet, according to US intelligence, this was partly orchestrated by Kremlin.
I think Peterson is doing his best to drum up controversy on this particular subject because he understands that there is a huge audience who wish to be scared and outraged of the SJW boogyman (I think it should be dubbed "outrageporn" or "outragebait"). In fact, the SJW boogyman is both very rare, and without elaborate arguments not very scary. If Donald Trump wanted me to call him "they" I would just shrug or laugh, however, I am not laughing at the idea of creating a national database and doing mass registration (violating the first and fifth amendment). Where the heck is the "don't want no gun database" crowd?!
In fact, the SJW boogyman is both very rare, and without very elaborate arguments not very scary. If Donald Trump wanted me to call him "they" I would just shrug or laugh, however, I am not laughing at the idea of creating a national database and doing mass registration (violating the first and fifth amendment).
By the way, the analysis that the "crazy left" is the reason people voted Trump in his other video is exactly the same kind of argument that the crazy left uses when someone confronts them with examples of "crazy left" behavior ("oh yes they are rioting and that is not right, BUT THAT IS BECAUSE...").