I thought Peterson's point was satisfactorily made, in my view he argued the following:

1. That blaming white people, or men generally, for the inequality across socio-economic borders in America is a simplification of a real and acknowledged problem.
2. That blaming white people for racism in the US is to paint the white population with the same broad-brush strokes that Dyson argued were so unfair in the first place. ie., Racism is unfair generalization about people based on race, we shouldn't do it, so stop doing it white people. Ha!

I dont think that Peterson focused on his personal feelings from the "angry white man" allegation, in fact he tried really hard to re-direct focus from a question of feelings, back to the core assertion that Dyson was not providing any argument or evidence for his assertions. In my view, it was Dyson who tried to focus the conversation on the hurt feelings conversation, like "oh, see you don't like it when I call you by your race".

The problem with Dyson's approach as I see it, is that Jordan's point was never that we should accept people hating others based on race, rather his point was that there does not appear to be a proven evidentiary argument from Dyson or elsewhere, which affirms the allegation that "were it not for priviledged white men, blacks in america today would be better off."

I think Peterson even said in his conclusion, is racism and hate real, of course, but something like "is playing the martyr what you want, or do you want a better life? If its the former, then focus on how "angry white men" hurt you and hold you down, but if its the latter than focus on what you can change today. Some of this summary is from my understanding of his wider body of work, and maybe I may have missed the mark slightly in summarizing his position, if so I apologize.

One interesting, slightly secondary point of debate is this, I think Peterson tried to focus the debate on the facts around political correctness being overcooked, and the need for us to recognize our own responsibility in our situation, and to the extent that we saw the debate degrade into pettiness is a win for Dyson, because it seems he wanted to make the conversation about how it hurts to be identified and marked on the basis of race, as if that in itself proves Dyson's contention, that white people are bad because racism exists.