Actually, I don't think it is impossible that male brains and female brains are different and that you might occasionally get a female brain in a male body or vice versa. The evidence is lacking but it doesn't seem beyond the bounds of credibility.
I don't understand that concept. Most of the studies I have seen show that in samples while there are some features in certain regions of the brain that are more common in one sex compared to the other, most people just have a mix of features. There is no evidence of any clear cut gender profile based on brain structure presumable because brains are plastic and develop based on their interaction with the environment. Hence, it seems unlikely that trans people have a gender identity that could be caused by having a brain linked to the sex that they are not.
And because people's brain structure, pathways and nerve connections etc cannot be characterised in a binary way when it comes to sex, one of the values society was trying to develop was that gender was artificial - so liking pink, soft, fluffy, pretty things or being caring and nurturing should not be pigeon-holed as gender characteristics that belong to the female sex whereas liking dirt and sport and being analytical and competitive should not be pigeon-holed as male characteristics. So we were trying to get away from the idea that people should be conditioned to act a certain way based on gender.
