Please correct me if I'm wrong, but my understanding is that there is literally zero scientific basis for saying "I am a woman" when you are in fact a man, whereas his claim of having "Korean DNA" does actually have a tiny tiny chance of being true. People with ancestors from certain places do have certain genetics in common, however trivial in the scheme of things.
There is a one in a million or 100 million chance that he does have half korean great great grandmother, and the tiniest touch of korean dna, whereas there is literally zero chance that he is actually in any way scientifically female.