I think the reason you don't want to engage is because you know he has a point and you don't have a response to his statement.

Your argument is based on a fallacy. Trans people ONLY want to identify with a gender they feel best fits them. Then people like yourself come along and create strawmans by equating "identifying with a specific gender" to "identifying as a helicopter" and other wild comparisons.

Also, science in genetics refutes your way of thinking.