If you were born with a snake, you are male.
If you were born with a vagina, you are female.
Is there an in-between? No, there is no other love organ that you could possibly be born with.
What you're born with is called
your love. Your
gender is not necessarily your love. Gender is how you act, think, talk, look, etcetera.
EVEN THEN, you still have it wrong. People can be born with both a snake AND a vagina. It's rare, but it happens. By your rules they have no gender, hence completely validating OP's freinds position. QED.