For years the radical women in the Women’s Liberation Movement were telling us that there IS no difference between men and women. They claimed that anything a man can do a woman can also do.
So now these same radical people are saying that gender is in your brain? Why would they even think that when they believe that there is no difference between men and women?
The common idea that transgenderism has anything to do with feminism and gender deconstructionism is, sadly, a confusion. As Rau (if I understood correctly) indicated, the groups are not the same.
That gender identity is a neurological phenomenon is not fronted by any ideology, but by research. Studies (originally dissection of deceased brains, later through brain imaging) have demonstrated significant differences between male and female brains, and that brains of trans women are closer to the female brain than the male. The accuracy of the autopsy study was 100% in predicting a transgender identity.
A later study indicates that there is a difference between trans women who are sexually attracted to males (the women in the first studies were all in this group), and those who are attracted to females. The condition seems to be differently caused in the two groups. However, this study also clearly establishes a neurological cause for the latter group.
Obviously, this conflicts with the common view among feminists that gender identity and gendered behavior are merely societal constructions. For this reason, many radical feminists
vehemently oppose transgender people, and reject these findings. In many ways, this research on transgender people
confirms Catholic teaching about the complementarity of the sexes; obviously this is unacceptable to radical feminists.
Mainstream feminism has however adjusted their views as a result of this research. But as with all ideology, the most extreme adherents will ignore or reject anything that conflicts with their view. Ironically, in this case, it has the same outcome among radical feminists and radical conservatives

. I also often even see the groups utilizing the same arguments, which is kind of entertaining.
Also, what is a woman supposed to feel like in a woman’s body? I’m a woman, and i don’t have a clue. And, of course, I also have no idea what a man is supposed to feel like in a man’s body.
This is a good question, which has sadly caused much confusion also among those who treat transgender people.
I think the best, and most universal, description of gender dysphoria is the unbearable turmoil caused by the body’s sex characteristics. The brain expects one type of sex hormones; when the opposite is produced by the gonads, turmoil ensues. Its presentation is often a strong dislike for one’s sexual characteristics, with a strong need to change them, and with a strong tendency to depression and anxiety (or worse) if no treatment is given. Dissociative symptoms like depersonalization are also common. The condition is disabling, and in some cases sadly fatal because of suicide risk. Hormone therapy has incredible effects in such patients - I know of cases where the patient had ended up with several, severe psychiatric diagnoses prior to receiving treatment for gender dysphoria, and could quit taking their cocktails of psychiatric drugs after a while on cross-sex hormones.
As to gendered behavior, yes, most patients report feeling inclined towards typical interests and behaviors of the opposite sex (I find “opposite sex” to be too simple here, but I’ll use it for the sake of simplicity), towards the clothing of the opposite sex, and so on. These are however incidental, and to some extent societally determined; what is feminine and what is masculine changes depending on time and culture. It probably has to do with naturally identifying with the girls instead of the boys (or the other way around), thus copying the “wrong” inclinations. But to some extent, interests seem to be “hard coded” - it has been demonstrated in behavioral studies that toddlers who are not “conditioned” in any way will normally, seemingly on instinct, choose toy cars and trucks if they are boys, and dolls if they are girls. Consequently, some inclinations are apparently caused by brain structure. Transgender patients are commonly reported to have “chosen the wrong toys” even as toddlers.
However, not everyone is stereotypically feminine or masculine. Traditionally, diagnosis has focused too much on these stereotypes, causing many patients who truly needed treatment to be denied such, often ending in tragedy. Just as among cis people, interests and behaviors fall within the whole spectrum of gender expression. In rare cases, patients feel fine just by taking hormones without transitioning socially. Generally, however, some level of change of expression and social role is required - everything from just appearing androgynous, to full transition.
It would be nice to have a better understanding of this mysterious ailment.
There are plenty of sources online, but a good place to start is the WPATH Standards of Care. It may not include as much about causes for the condition, since it is largely a guideline document for treatment, but it describes the spectrum of how gender dysphoria presents, and the different levels of treatment, well. If I remember correctly, it also has a lot of citations to studies more directly linked to causation and so on.
Other than that there’s a wealth of studies, books and so on. I don’t have any links available from where I’m at, but if you Google around a bit, you should find a lot of material. But again, I’d recommend starting with the SoC - it is the universal guideline for those who treat transgenderism, and as such a great place to start.