Do you support applying that same logic to transracialism? E.g. white woman identifying as a black woman?
If it's purely a racial/ethnic kind of thing that's about your genetic heritage, I agree it doesn't make sense to apply the same concept. It's like the distinction between sex and gender I mentioned above, trans people identify as a specific gender regardless of their sex, and I think people can identify with a specific culture regardless of their race/ethnicity. To better complete the analogy, I could definitely imagine a white person growing up in Japan their whole life and feeling a general unease about the mismatch between their cultural identity (Japanese) and their race/ethnicity (white), and in cases where that unease is severe enough, potentially being willing to go through surgery to better reflect their identity. Dysphoria over racial/cultural mismatch (if it even exists, idk) seems much less common than gender dysphoria, but I don't see why you wouldn't apply the same logic to both.
> you spend every day of your life fighting the nagging feeling that you don't actually identify with gender you're "supposed to" identify with
I have no problem with believing that some people aren't the gender they physically represent. But, in my mind, arriving to the conclusion that 'I don't identify as a male, therefore I must be female' isn't right.
> And why am I a woman? Because I'm a woman
Again, they don't actually know that they're a woman. They know they're not male, for sure, and I'm fully on board with that. But insisting that they're female... I'm not sure. Is 'trans woman' not sufficient?
Benjamin Boyce has a YT channel that deals with some of this stuff that I watch occasionally to try help understand.
I think for trans women, it isn't so much a conclusion following from not identifying as male as it is simply 'I identify as female', but this runs into the same issue that you brought up in your first comment of not actually knowing what being female is. But then again, doesn't knowing they're not male imply they know what being male is despite not being male? I think it's just too philosophical of a point for most trans people to concern themselves with when they're dealing with who knows how many other issues.
I recommend either reading or watching more stories about trans people's personal experiences if you want to get a better sense as to why people feel that way, as different people probably have different reasons. I don't personally have any recommendations (the quote I mentioned earlier was a small comment from a video on a completely unrelated topic), but thanks for the recommendation for Benjamin, I'll check him out!