First, I know exactly the brain scan studies you’re referring to, and the study makers made the criterion as such for those results to happen, and no other scientists could replicate the results. As there are differences in a persons brain depending upon male and female.

Transgender brain studies, especially those on trans women who are sexually attracted to women (gynephilic), and those on trans men who are sexually attracted to men (androphilic), are limited, as they include a small number of tested individuals. The available research indicates that the brain structure of androphilic trans women with early-onset gender dysphoria is similar to the brain structure of cisgender women’s and unlike cisgender men’s. It also reports that both androphilic trans women and trans women with late-onset gender dysphoria and who are gynephilic have different brain phenotypes, and that gynephilic trans women differ from both cisgender male and female controls in non-dimorphic brain areas. Cortical thickness, which is generally thicker in cisgender women’s brains than in cisgender men’s brains, may also be thicker in trans women’s brains, but is present in a different location to cisgender women’s brains. For trans men, research indicates that those with early-onset gender dysphoria and who are gynephilic have brains that generally correspond to their assigned sex, but that they have their own phenotype with respect to cortical thickness, subcortical structures, and white matter microstructure, especially in the right hemisphere. Hormone Use can also affect transgender people’s brain structure; it can cause transgender women’s brains to become closer to those of cisgender women, and morphological increments observed in the brains of trans men might be due to the anabolic effects of testosterone.

And this is just about the brain, there are genetic factors in those whom are trans as well, which means, by the way, that it isn’t just an “idea” that does not reflect reality, their genes and phenotypes match up more directly with their gender identity (FtM which are trans men or MtF which are trans women) than it does their birth sex or even those of their birth sex that are used as controls. Note: in the below quote, the use of transsexual means someone whom is transgender, the term is just an older one.

A 2008 study compared 112 male-to-female transsexuals (MtFs), both androphilic and gynephilic, and who were mostly already undergoing hormone treatment, with 258 cisgender male controls. Male-to-female transsexuals were more likely than cisgender males to have a longer version of a receptor gene (longer repetitions of the gene) for the sex hormone androgen or testosterone, which reduced its effectiveness at binding testosterone. The androgen receptor (NR3C4) is activated by the binding of testosterone or dihydrotestosterone, where it plays a critical role in the forming of primary and secondary male sex characteristics. The research suggests reduced androgen and androgen signaling contributes to the female gender identity of male-to-female transsexuals.

This is for trans women, this next one refers to trans men.

A variant genotype for a gene called CYP17, which acts on the sex hormones pregnenolone and progesterone, has been found to be linked to female-to-male (FtMs) transsexuality but not MtF transsexuality. Most notably, the FtM subjects not only had the variant genotype more frequently, but had an allele distribution equivalent to male controls, unlike the female controls.

Therefore, there is not only psychological basis, as well as basis in brain structures of trans people that confirm these people are their gender identity, but there are also areas where there is genetic basis for trans people. Not to mention, your continued use of the word “delusion” for such a thing as this is very ableist, as you insinuate that trans people are detached from reality by doing so, when in fact, much of the scientific reality of their bodies genetically and within their brains matches up with the gender identity they want to present as instead of their birth sex. Meaning the only things that don’t are their physical characteristics and the way they reproduce. Which, by the way, I do agree an egg and sperm are necessary for reproduction, its just sex is no longer the only way by which you can do that. Otherwise, infertile women or men would never be able to have kids despite an intense desire to do so. And, quite frankly, I do however disagree entirely with the notion that those sex characteristics for reproduction mean sex or gender are in anyway binary. Because frankly, they’re not. Its more like Bimodal distribution than a binary. Because Binary means only two options, with no variations. Bimodal distribution means there are two likely options, but they’re not the only ones and it makes up for the variations we see in the genetic make up of individuals, the different hormonal make ups of them, etc. Far more neatly and accurately than sticking to such a strict binary.

Here’s your response. At this point I highly doubt that I’m going to end up changing your mind about literally any of this. As you seem pretty rigid in your idea that the trans identity and by extension the trans community are all delusional for trying to match the gender identity they are. But I will leave you with quite the set of parting gifts.

1. Respect the name and pronouns they use, no matter what. Because socially transitioning is one of the biggest steps to take after just coming out, and it can make or break someone with crippling dysphoria to be referred to by their chosen name instead of their dead name, as well as their proper pronouns instead of the ones the were forced to use at birth, which could wreck their mental health if you do so, and the trans suicide rate is still something to watch out for.
2. Sex is different from gender. Gender is entirely socially constructed and enforced. And there are plenty trans individuals who don’t want to adhere so strictly to gender roles of their gender identity or the stereotypes that come with them and still be seen as passing. But transphobes as well as intolerant or disrespectful and judgmental people (including those like you who believe all trans people are delusional) are actually what enforce those stereotypes as the second they don’t use them, many of them no longer pass, and people see it as an opportunity to misgender and even dead name the trans person. Which I’ve already stated can be harmful to that persons mental health.
3. Also, this is pretty much a rule of thumb for me. But I wouldn’t be friends with you. And I frankly couldn’t be. Because I don’t make a habit of making friends with those who hold or perpetuate harmful, bigoted, or hateful ideas. And you perpetuate all three of those things purely on the way you word your responses and arguments when it comes to trans people, whom are a marginalized group.
4. Lastly, if it walks like a duck, talks like a duck. We wouldn’t call it anything except a duck. So if it sounds like anti-trans sentiments, works just like anti-trans sentiment. It is anti-trans. You don’t decide that label. You can refute it all you want. But so would someone homophobic deny being a homophobe. Or someone racist deny being racist(unless they’re proud of it). Your ideas line up with being anti-trans. You can deny that till the cows come home. Its not going to make anyone see you as anything but anti-trans, except for circles who are also anti-trans, who will slap other labels on to disguise it.

And with that. I bid you adieu. As I’m not going to continue trying to educate or debate someone who doesn’t really want to do those things honestly or completely.