That's a good study. I'd been reading: Two minds The cognitive differences between men and women
I guess currently all we can say is that even if there are differences they do not seem to be significant enough to allow us to associate any other assumed differences with them.
What causes anyone into "feeling" that they are a man or in "feeling" that they are a woman? If it is not their body or their brain, then what?
What, if anything, does it mean to "be in the wrong body"?
Why people think what they think or believe what they believe regardless of the lack of evidence for their beliefs or even evidence to the contrary is a complex area to unpick as there are probably many factors that contribute to our perspectives and beliefs about anything.
For example, unlike many other people, I would choose nuclear obliteration over giving in to Putin's threats. I have no idea why my feelings of aversion to placating Putin are more than my aversion to nuclear war. I don't choose my feelings or thoughts. I don't think the reason I think that way is based on my gender. Is there a biological reason for my preference?
That is not to say that I can't overcome my instinctive preference for risking nuclear war now or that I can't decide that I should make a choice based on reasons such as estimates of probable deaths due to future invasions by dictators vs deaths by nuclear war now or some such calculation. I can recognise that my gut emotional response of not giving in to dictators may not be the right response if I was the leader of a country rather than an ordinary citizen. So environment and circumstances have a lot to do with our perspectives.
Your link seemed to identify XX and XY chromosomes and hormones as 2 main factors to the reason for any differences between male and female brains. Trans identifying individuals are biologically male and female and seem to have the cell biology and hormones that correspond with their sex. So it would seem that a neat biological basis for their belief that they should be the opposite gender has not been identified. Your link suggested altering a gene has an effect on the maternal instincts of mice. But still not sure why this would correspond to a particular gender identity in humans. Animals don't have gender identities.
A far as I can see gender is a social construct - a bit like being a punk or a goth. There is no need to identify as a punk or a goth or any other category but some people choose to do so for complex psychological reasons that it makes them feel good to do so.
It is possible to like certain aspects of the punk or goth look and tastes without actually identifying as a punk or a goth. The appeal of certain looks and tastes may have biological basis - the current thinking is our tastes are a mix of nature/ nurture. People have the option of dabbling in the punk or goth look when they feel like it without permanently altering their outward appearance - yet some people choose to embrace the identify more enthusiastically than others and do permanently alter their outward appearance to match what they feel like on the inside. Why some people are more enthusiastic / "obsessive" about these identities, especially as teenagers may be due to their insecurities and search for identity in their teens.
I remember when I was a teen I liked black clothes - probably because i did not feel confident enough in myself to wear bright clothes or the fashions for girls at the time as I thought I looked stupid trying - I thought I couldn't pull it off. A boy I was friends with made a comment that I was into Goth style - and I had never considered myself a Goth but it sounded cool , so I adopted it as an identity for a while, because it made me feel more confident and gave me a reason to not experiment with the bright fashions of the 1980s that I felt made me look stupid. I also used to dress more like a boy - because the clothes were more comfortable and draped well so you felt less self-conscious. As a child I even wanted to be a boy until I reached puberty, because I enjoyed playing football with my brother and his friends and girls games and playing with dolls seemed very boring in comparison. Once I reached puberty I just accepted I was a girl who liked doing some of the stuff boys do and don't like doing some of the stuff girls like to do. I have no desire to nurture and look after someone else in terms of feeding them and worrying about their creature comforts or feelings, but do have a strong protective instinct to people being taken advantage of. I have no interest in buying lots of jewellery or bags but do like being tidy and clean and making my room look nice etc and dislike having to share a space with untidy men and women. So I have no idea why some people have a need to categorise themselves into any particular gender stereotype.
There is a suggestion that autism - which can manifest as obsessive behaviour in relation to categorising things - could be part of what drives trans-identifying people to thinking they are the 'wrong' category in terms of gender because they associate their tastes with the opposite category/ gender.