You slipped in "based on sex" for an intentional reason that I'd like you to share with the class. Say, is your opinion of the "sex is an immutable characteristic and fixed at birth and therefore trans people are invalid and should..."? Or maybe I'm just reading into your wording a little too much.
You're talking to a trans woman by the way. Just thought I should throw that out there just in case you want to hurl some insults at me while you're at it too :)
Congratulations on immediately being vindicated :/
In humans and other mammals the immutability of sex is a fact, not an opinion. We are not a species of sequential hermaphrodites.
The cultural artefact of people identifying themselvee as the opposite gender is a different type of concept to this. It's more of a sociological or psychological phenomenon.