The point is they are identifying as something other than what they are in reality. That's the whole point.
If someone says, "I identify as a millionaire!," the proper response is, "That's great but you're not a millionaire."
Likewise if a man says, "I'm a woman!," the proper response is, "That's great, but you're not a woman."
It's cute you think you are in a position to explain something to me.
Yes, I am fully aware of the point you are trying to make, but the situations aren't analogous. I do understand you won't be able to follow along with the rest of this post, but I feel compelled to write it all the same.
Acknowledging transgender identities isn't based merely on the idea that we say we are women or men.
"But wait!" you cry, "don't transgender people argue self-identification is all that matters? Is all that is needed?"
Kind of. The acceptance of transgender identities in principle isn't based merely off of self-identification. There is a history of practical medicine and scientific research which supports the validity of transgender identities. However, there is no satisfactory test to objectively and indisputably measure that an individual person is transgender. We rely on self-reported feelings for diagnosis of gender dysphoria. We rely on self-reporting for understanding people's gender identities. This approach is not unique to transgender identities.
But even if we set that aside, to say one is a millionaire at the bank is a statement of the wealth one possesses in their account. Factually, the money isn't there.
But to say one is a transgender woman when talking to one's doctor and seeking medical transition, let's say, is pretty much doing the opposite. It's saying I have a female gender identity, but my body doesn't align with that.
If we translate that back to the millionaire analogy, it's like walking into the bank and saying, "I a millionaire's identity, but it troubles me that my identity doesn't align with my bank balance." And to that the bank says, "Well, we don't have the means to make you a millionaire, but we can take what you do have, set you up with a financial advisor and get you as close as we can. Not only that, but if you show up the the yacht club, we won't talk down to you like you're poor as shit because we recognize--despite your bank balance--we recognize you're cut from the same cloth."
But even then, still not analogous. There are reasons to believe there is a biological root to gender identity and that a misalignment between neurology and the rest of our physiology is plausible. We also recognize a shit ton of what we label 'male' and 'female' or 'masculine' and 'feminine' has fuckall to do with anatomy or biology. A lot of it is social convention which can be applied to someone regardless of what they have going on in their pants.
But that doesn't apply to being a millionaire. There is no known biological root cause to identifying as a millionaire neither is there a reason to believe one exists. Millionaire, by and large, is just a singular statement on how much wealth you have.