One thing I wonder about whenever "the brains of men and women have systematically different structures" comes up, is what structures do the brains of trans people demonstrate?
> For this purpose, we analyzed a sample of 24 cisgender men, 24 cisgender women, and 24 transgender women before gender-affirming hormone therapy. We employed a recently developed multivariate classifier that yields a continuous probabilistic (rather than a binary) estimate for brains to be male or female. The brains of transgender women ranged between cisgender men and cisgender women (albeit still closer to cisgender men), and the differences to both cisgender men and to cisgender women were significant (p = 0.016 and p < 0.001, respectively).
Why do you wonder that? Because if brain structure is shaped by environment then it tells us nothing. If it’s not shaped by environment and brain structure is a fundamental biological difference then it provides some signal.
I don't think it matters so much to me why someone has a particular gender identity — if that's physiology or environment — but I think it would still be interesting to be able to determine independently of self-identification.