I don't think anyone knows exactly what these differences mean, or why they manifest as a desire to wear women's clothes rather than, as, say, a desire to take care of people.
I'm sorry but this is bad science. Setting aside the questionable nature of any studies on physical differences of the brains of those attracted to women vs. attracted to men, attributing a desire to wear women's clothes to it is a giant leap. Even in the premise you lay out, you'd have to establish that the claimed difference between same-sex and opposite sex attracted was specific to transwomen and not just males in general. There are plenty of gay men who don't cross-dress.
I think it would be interesting to understand the brain basis of dysphoria with one's body. I would have predicted a common region of the brain being affected as compared to people who have dysphoria with non-gendered body parts. But I don't know if anyone is doing that research.
Here also there's a questionable assumption which is that trans = dysmorphia. In adolescents and particularly girls, a form of body dysmorphia does appear to undrly a lot of trans identification as young girls find themselves uncomfortable with their developing bodies or the attention it brings. But adult men who transition to female in my experience, do so overwhelmingly for sexual fetish reasons. Of all the adult male trans people I have known, precisely one may have had some dysphoria. (And even then, he hardly acted like a woman. Least ways I've never had a female collegue who'd tell the people on the call she wasn't wearing anything below the level of the camera).
There is a neurological correlation with identifying as trans as adolescents. And it's autism. The correlation is very high. Autism isn't fully understood and may be developmental, but it doesn't equate to being trans. What it does is create a risk factor because an autistic child, especially as they hit puberty, often finds themself struggling to understand social interaction and feeling out of place. Suddenly a group come along (usually on Discord) and tells them there's a clear and simple explanation for that which is they've got the wrong brain. Instantly they have (a) an explanation they can understand, (b) social approval from teachers and the media that tell them they're special and (c) a set of social stereotypes that they think they're supposed to behave like. It's like a rock to a drowning man. In this model, which matches my observations, neurological issues don't lead to a "desire to wear women's clothes". They create an exploitable situation for others with their own interests to take advantage of.
Also, and I have to say this, your implication that "taking care of people" is a biologically feminine trait is also something I'm not inclined to just accept. It's a human trait, I feel. Men typically express it differently in our society but the idea that there's a female brain type which cares about people more and a male brain type which cares less, is offensive, you don't think?