That's just plain wrong. Mental properties in general (e.g. personality) are not easily measurable, but that doesn't mean they don't exist (or can't exist without a non-material soul), and I see no reason to think that an innate sense of gender would be any different.
In any case, while gender is not directly measurable, it does seem to correlate with some aspects of brain structure. A number of studies have shown that, at least in some respects, the brain anatomy of transgender people is more similar to that of cisgender people of the same gender than those of the same sex. It's clearly more complicated than trans people having one type of brain in the other type of body, but something sort of like that is going on. See https://www.scientificamerican.com/article/is-there-somethin... and the links at https://sitn.hms.harvard.edu/flash/2016/gender-lines-science....
But whatever the basis of transgender identities is, it's clear that something real is going on. Dismissing trans people as "simply mistaken" is, well, simply mistaken.
EDIT: I should probably point out that the idea of someone developing some male-type features and some female-type should not be particularly surprising. Sexual differentiation is complex and has a lot of moving parts that don't always operate completely in sync. For example, a genetic male with complete androgen insensitivity syndrome will generally develop male-type internal organs (i.e. testes) and female-style external anatomy (a vagina, generally female appearance, etc).
In any case, while gender is not directly measurable, it does seem to correlate with some aspects of brain structure. A number of studies have shown that, at least in some respects, the brain anatomy of transgender people is more similar to that of cisgender people of the same gender than those of the same sex. It's clearly more complicated than trans people having one type of brain in the other type of body, but something sort of like that is going on. See https://www.scientificamerican.com/article/is-there-somethin... and the links at https://sitn.hms.harvard.edu/flash/2016/gender-lines-science....
But whatever the basis of transgender identities is, it's clear that something real is going on. Dismissing trans people as "simply mistaken" is, well, simply mistaken.
EDIT: I should probably point out that the idea of someone developing some male-type features and some female-type should not be particularly surprising. Sexual differentiation is complex and has a lot of moving parts that don't always operate completely in sync. For example, a genetic male with complete androgen insensitivity syndrome will generally develop male-type internal organs (i.e. testes) and female-style external anatomy (a vagina, generally female appearance, etc).