Even if the brain of a person who identifies as trans were closer to that of their identified gender (Narrator's voice: "They're not"), who is to say that these minor differences override than the vastly larger biological differences of sexual organs, hormone levels, etc.
He goes off on a tangent about souls which for me is irrelevant and also not a basis for argument, but his initial response to point out that she's now arguing that gender IS determined by biology is a good one to make and one I made years ago. I have found in general though that the science for brain differences is so weak that I prefer to just focus on rebutting that and keep it simple.
There ARE different tendencies between male and female brains, but my understanding is that they are developmental rather than inherent. By which I mean the different environments - size of the brain case, the bath or hormones in which they operate - lead to slightly different outcomes. A red rose was always going to grow red and not white, but the difference between male and female brains is more akin to two red roses grown in slightly different conditions.
And I've never seen any evidence that the brains of trans people follow the opposite tendency to their actual sex. And indeed, as we are ONLY talking tendencies and not clear separation that wouldn't really be meaningful anyway as a trans person would merely be an outlier for their sex amongst many other outliers who WEREN'T trans.
Of course that last point would suddenly have TRAs pipe up that other outliers were trans but just didn't know it, which is patronizing.