Yo, I lurk some of these places.

You're confusing two concepts. Average differences in personality are not the same as gender identity. It is possible to be a feminine man or a masculine woman. None of that makes a feminine man somehow really a woman.

Innate gender identity doesn't exist. Nobody has a magic display in their head saying UR A GIRL. That does not mean there are no innate differences in a statistical sense. Clearly there are.

https://www.scientificamerican.com/article/is-there-something-unique-about-the-transgender-brain/

You should read these studies carefully. There are no differences we know of that can't be explained by sexual orientation.

To be really clear: transsexuals are mostly either

1. just gay men or lesbian women who prefer living as the opposite sex, due to being very gender nonconforming
2. straight men with a sexual fetish that involves becoming women, called autogynephilia.

Gender identity doesn't need to exist to explain it.

Question; if innate gender identity doesn't exist and is the result of socialisation, then how come David never identified as a female?

Lots of reasons. He was a fucked up little kid. He was pissing through a hole in his abdomen and was brought up as a boy til age 2.

But in general what happened to Reimer was weird. There are kids born with a nasty condition called cloacal extstrophy. Boys born without genitals basically. They're usually reassigned to girls at birth. And most, but not all, stay that way. So... gender identity is bullshit.