As a point of argumentation, why would anyone put "impressive credentials" or "intellectual intelligence" (arguing from which is a well-recognized logical fallacy) up against "lived experience" (i.e. first-person anecdote, which is well-recognized to be biased and unreliable in certain cases, but can be used in some valid arguments)?

Of course, when people feel they must be right because the alternative (e.g. they are being unjustly cruel or supporting the same), they tend to throw a lot of illogical junk out as arguments. And accepting something Peterson says because it fits their biases, not because it's well-supported, is par for the course.

In contrast, on topics that Peterson speaks on, he often is backed up by a good deal of research. Not always! But often. If one happens to end up arguing with Peterson himself, one would need to bring something far more reliable than "lived experience" to the table. Nonetheless, he seems relatively reticent to advocate for cruelty, and to be genuinely moved by people's suffering. I think the problem is more acutely with his fans than with him.