edam
I'm not convinced either, but for the sake of discussion, I don't even see how its relevant even if it was possible.
Looking at the structure of the brain and its chemistry only tells you about the biological brain, and not the mind.
Therefore, if there was such a thing as a 'female brain' or a 'male brain', it would be just the same as having 'female genitalia' or 'male genitalia', or internal reproductive organs, or bone structure etc. etc.
Which means that a biological female (XX) for example may theoretically have 'the wrong brain' and yet they would still be biologically female, because biology does allow for occasional variations.
This would be the same sort of mismatch we already find occasionally in for example biological males (XY) with androgen insensitivity (who may have a vulva instead of a penis). They are still male (XY), have testicles, no internal female reproductive organs, but one biological part does not match - the external genitalia.
Using the same argument, a biological female (XX) for example, who was found on a scan to have a 'male brain' (whatever that may be), would simply have one mismatching biological part, and would still be biologically female (because the only consistent biological factor is chromosomes - all other biological features are usually there, but not always).
I think people get confused because they think of the brain and the mind as the same thing. The brain is a physical structure and is biological. The mind is not physical and consists of intangible things such as thoughts and feelings.
The brain can influence the mind and vice versa, just as the rest of the body can influence the mind and vice versa. But the brain is still just another biological part of the body.
A brain scan will never be able to tell you your gender-identity, because your gender is what you say it is (based on your feelings in your mind). The two things may happen to match, in which case great. :)
But in a case where a biological brain scan did not match your internal gender identity (mind), then I would expect mind to have the final say... which means gender identity is about the mind and not the brain (though it may be influenced by it).