If there is no neurological sex (if your contention is true), then it must be the case that all it takes for someone to be meaningfully "woman" is to socialize with women as their peer group and be exposed to estrogen rather than testosterone: trans women are then meaningfully women.
If there is a neurological sex (if your contention is wrong), then it must be the case that not only are transwomen women, but that they are born that way: trans women are meaningfully women and it is even more awful to force them through the wrong puberty.
Alternatively... biological sex influences the experiences that people have
Except when it doesn't... say
for fucking trans people, or for instance, those with reconstructioms following an at birth DSD diagnosis...
, and this neural plasticity produces differences. Additionally, hormones DO affect the brain.
Except that the hormones DO NOT directly affect the brain development, especially at the epochs of life we are talking about. It's more a game of "mouse trap", where one thing impacts another and so on until a result happens. Spoilers here, though: half the time the reaction in the game never makes it to the end point, and the basket never comes down. Biology is a lot more reliable, but nothing is perfect. As evidenced by the facts of the DSD population.
What you're arguing, however, is that there's some innate brain sex that is distinct and separate from biological sex...
No, I'm arguing that both are biological. Because neural development is just as biological as gonad development.
and that for some people this special "brain sex" makes them fundamentally as much of their "brain sex" as a person who is biologically that sex.
If there is a brain sex, it has biological roots. Period. They are both "biological". The question at play here is which biological entity has more meaning to how we interact with people. My contention is that we interact with "who someone is", not with "what is in their pants" 99.99% of the time.
In clearer terms... You're arguing that there is some innate from infancy "male brain" that exists with zero connection to the body,
Again, no. I'm arguing that while the body significantly impacts probabilities as a function of prenatal hormonal exposure and then a practically goldbergian process of chemical potentials, that the steps between "DHT" and "brain formation" are vulnerable, and in .42-2% of the population have fallen victim to such vulnerabilities of the process to being waylaid by chance.
and is not affected by the chromosomal make-up of the person in question
No, I'm arguing that the linkage is probabilistic, not absolute. Do you even know what probabilistic means? I'm starting to doubt. I've used it several times now.
and remains resistant to the hormones to which it is exposed in fetal and pubertal development.
Not resistant. Just not deterministically influenced by hormones at the stage of the process where the actual structure happens.
And that this "male brain" is so strong a force, that it overrides the female body in some people
Again, you fail completely and utterly here. "The body" (genitals) doesn't get "overridden" because the brain is not the genital. They are separate and distinct structures formed by very different processes.
, as well as the female experience of having a female body and the experience of being a female in society...
Sorry, no. Trans children do not have a "female body' to the extent it matters except to the extent that it creates difficulties or eases those difficulties with regards to how they pee. They don't have breasts. They don't 'lack' an adam's apple any more than their peers. Provided they are allowed to interact as a girl with other girls, present as a girl, learn how to be a girl, a trans girl prior to puberty will have the same experience any other girl does, except for the slight detail that she can write her name in the snow*.
in such a way that this person is fundamentally "male" as much as a person who has a male body and experiences is.
You put WAY too much importance on what is between someone's legs. I didn't know what my dick was capable of doing until I was 16. I didn't care about it. It didn't determine how I acted. What determined how I acted was my brain, how it was socialized, and how I assumed I ought act as a function of my innate neurological biases.
Do you also argue that people who identify as otherkin have some a fully or partially non-human brain?
Nope. I assume that they have the right to their own identity though, and that their socialization in their peer group is just as significant to who they are as your socialization in your peer group.
There is definitely a phenomena wherein some segment of humans identify, unbidden, as something along the lines of "otherkin". They did this long before the internet ever existed, before even the written word, and there is absolutely some biological basis for neural predispositioning towards that end.
It doesn't mean they are, strictly speaking non-human, but it does imply there is more going on here. To go back to your schizophrenia example, while schizophrenia does not speak to the reality of the voices someone hears in a universal sense, it absolutely implies that there is a neurological phenomena driving these similar outcomes.
Edit: *and after I wrote this, I realized another important facet about growing up a trans girl: they will also be molested, harassed, and raped to the same extent their cis peers are too. Because it's not like predators, assuming that the child's privacy is protected by their parents, will know until it's too late for the victim regardless, and it will suck just as bad. Potentially worse.