Question: Trying to figure out the fallacy here, I can't put my thumb on it.

Argument from Ignorance. The assumption of a conclusion or fact based primarily on lack of evidence to the contrary.

Scientifically, this is a strange dialog because gender (not biological sex) is a socially constructed concept to which no "proof" can exist outside of wide-scale agreement. A gender is XYZ because we, as a society, has agreed that it is.