I think the idea of trans people have a female and male brain like the sex they want to be is a boomerism at this point. Younger trans people don't even make that argument much anymore (it's not nonbinary enough).
People like that undoubtedly exist (as a result of prenatal hormone exposure caused by various factors,) but they amount to a rounding error compared to the number of people in other cohorts who comprise the trans movement. These cohorts have been described by previous posts so I won't go into detail about them, but it is safe to say that many of the "early adopters" among them became drawn to transgenderism some time in the early 2010s, when Tumblr was a sort of nexus for the wider radical feminist community.
Regarding Tumblr, one thing I often see overlooked when talking about this sort of thing is the way that a website/platform's feature landscape impacts the type of users it attracts and deters. I can't speak from personal experience as I didn't use the site at the time, but looking at archives of the site can tell us a few things:
1) In many of the early years of the modern trans phenomenon, it required an account to view content on the platform. This would cause anyone who didn't care about creating a persistent identity to turn away.
2) When searching for content to view, the content presented to the user would be done so via a recommendation engine. This indicates that the users were subjected to opaque algorithms that recommend them content based on unseen parameters of their persistent identities stored server-side.
3) Every user had their own fully-customizable blog. Background, font, layout, images, everything. This meant that narcissistic and people obsessed with broadcasting their own identity were drawn to it, and those who didn't care for it were nudged away.
If we put these facts together, the conclusion is that Tumblr drew in self-absorbed narcissists, pushed everyone else out, and used a recommendation engine in order to drive user behavior in ways that are impossible for us to be certain of. The end result was a competition between narcissistic individuals to see who could stand out the most and win the most approval from their peers.This is the environment that the modern-day transgender movement, alongside the broader radical feminist movement, was incubated in before being released onto the public.
So that explains (at least partially) how the trans movement and all the other insanity associated with it was created, but it does not explain why it was done. In order to explore that, it will be necessary to look into key people involved at Tumblr at the time. I will probably post more about this later, but an easy one for you to start with is the founder:
https://en.wikipedia.org/wiki/David_Karp