I'm more concerned about the ignorance of biology here than anything about this fight. You lie to yourself about how race works, and biology too. In this case you similarly appear to think that people can choose their own biology.
Trump is correct that the person transitioned by calling themselves female. The primary key to sexuality is genetics, not genitalia. If you have XY chromosomes then you are biologically male. If you have XY chromosomes and are born with female genitalia, then you are a biological male born with a physiological mutation. If your parents dress you as a stereotypical female as a child due to that, that makes them mistaken.
Considering that this person knew that they had XY chromosomes, and proceeded to represent themselves as female, they therefore transitioned to their preferred social construct gender.
For your argument to work, you would have to argue that genitalia matters more than the primary genetic distinction between male and female that is inherent in all cells with chromosomes, which is laughable, to say the least.