Yes, a philosophical argument.
If Doctor Upton, a man, claims to be a woman, he is wrong.
[I tell students not to use scare-quotes, btw; I'm not saying he is 'wrong', just that he is wrong. When you write of his subjective 'knowing' of self, you aren't talking about anything he knows, are you? (Because if you were, you wouldn't need the scare-quotes.) So what are you talking about? ... This is an example of why I disallow student scare-quotes: they cause confusion and allow sloppiness. Do you understand this, @Tandora?]
Doctor Upton, a man, cannot know he is a woman, because "Dr Upton is a woman" is false, and knowledge requires truth.
Doctor Upton might well think he is a woman, or believe he is. And we can agree he does. What we (and the good doctor) might disagree about is whether his belief is true or not.
I say a man cannot be, or become, a woman, which is why "Dr Upton is a woman" is false. You?
Of course it all comes down to whether a trans woman is a woman or not. That's why "TWAW" has such a history, and why "No Debate" was so current a while since.
All the chat about "subjective 'knowing' of self" and such is just so much smoke and mirrors put about by those whose philosophical arguments aren't up to much. Sorry, @Tandora.