I bet molestation and abuse explains a large percentage of Peterson's opposition.
You can tell all these extreme leftist protestors are mentally insane. You know that they didn't have a good childhood. Some maybe too spoiled, some too abused and molested and some all the above.
I would say that the level of social pressure around universities and other places, where this type of an ideology is slowly being cultivated, is such that even a person without a direct emotional investment to the ideology, can easily become convinced about its righteousness, to the point where he will become as radical as the extremist, in an effort to become accepted within an in-group. A "normal" kid with "normal" parents (in the traditional sense) can come to adopt behaviour that we associate with "social justice warriors", if he is constantly surrounded by other people of that sort, and dependent on them in order to advance his life and career.
Those are the kind of people that, once separated from the "leftist" construct, can still be convinced about the potential flaws in their world-view, though only if they are separated from the group and allowed to receive and respond to information as an individual person, rather than as a part of a greater collective which seeks to suppress one's abilities to form conclusions in order to enforce a "hive" mentality.
Once you've become invested to an ideology through an emotional, almost a religious experience of sorts, it is impossible to convince the person one way or the other through arguments. These people could only experience an "awakening" of sorts, once they are forced to go through equal, or greater, emotional turmoil. Only then, they may change their mind. It would not, at all, for example, surprise me to see a hardcore social justice warrior turning into a hardcore Christian on a moment's notice, after what they deem to be a "life-changing" event. On the other hand, the kind of a person who does not truly have an emotional investment in their ideals and principles, is less likely to become hardcore anything, unless forced to as a result of the surrounding social pressure.
When dealing with a radical person it is important to be able to evaluate whether they have been radicalized through emotion, or through pragmatic necessity in order to advance in the social ranks. One must be able to adjust his methods accordingly, when dealing with different types of people, with different motives. One can be convinced through logic, one can be convinced only through emotion. For most people, of course, you will need a mix of both, well-constructed principles empowered by conviction.