Emily's Cat
Rarely prone to hissy-fits
It's actually quite funny how often we see this "exist" formulation. Indeed one of the most common claims that TRA have in their bag is that somehow we are denying that they exist, which of course would be pretty foolish. They exist and they are human beings, quite obviously.
Of course, what they really mean is that we are denying their self-identified gender and at that point the response is, "No ****, Sherlock."
It's not even that - for the most part, nobody generally denies that they feel like they are whatever gender they have chosen. With some exceptions where most people think the person is lying* we pretty much accept that they feel however the hell they feel.
What is being denied is that their feelings - their belief - makes them a different sex, or that their feelings - their belief - is more important than sex.
There is no other topic in the developed world where a person's unverifiable internal belief is granted supremacy in law over the material reality of other peoples' lives.