You brush over this way too quickly.

In some other places you make some good points (and in yet other places you make some not good points), but this one is skating around the crux of the issue without addressing it whatsoever.

The question is whether brains are sexed, and if so, if the sexing includes an intrinsic affinity with a sexed body; and if both are true, whether in practice people with fairly typically male-sexed brains with male-anatomy-affinity end up in female bodies, and vice versa.

If this is true, then your entire argument is invalid. Because the premise is that people have one sex for their entire body, brain included.

That there could be a mismatch in some cases is not a completely outlandish thing to consider. Scientists routinely make flies where different body tissues have different sexes in order to understand where sex-specific differences come from. Flies with female brains and male bodies are just a matter of expressing the right regulatory factors in the nervous system. Furthermore, that there exist cases of DSD indicates that the normal regulatory machinery can go awry at the whole-body level. So how sure are we that it doesn't also go awry in tissue-specific ways? You certainly have people with a normal female body but not a normal reproductive system, as another example of a tissue-specific failure of the sex determination pathways. Are there cases where you have what is effectively a female mind prepared to process input from a female body which finds itself in a male body, or vice versa?

Especially because people with gender dysphoria report a subjective sense of exactly this phenomenon, I don't think it's fair to simply sweep aside the concern in a parenthetical that hardly even addresses the issue.

There are other problems with some of your characterizations (mostly in neglecting to consider the situations where someone has transitioned successfully to the point where the perception of their gender matches their new gender), but not considering the possibility of a brain-body mismatch when trans people frequently say that is exactly what it feels to them is going on is by far the largest flaw.

(Note that one may need different arguments for different trans people if there are differences in the underlying biology. For instance, one can imagine cases where some brains are sexed, some are genderfluid intrinsically and latch on to the sex of the body, some are genderfluid intrinsically and get confused and are transiently backwards to the sex of the body, that some brains are sexed but have developed neuroses that cause them to reject their sex, etc. etc.--to be comprehensive, one would need to investigate whether each of these possible phenomena were real, and if so, consider how to handle that particular case. The answers may not all be the same.)