Aristotelian Laws of Thought and Logic:
Law of Identity: A concept or object that shares the same properties are identical. "A is A, B is B."
If A does not share the properties of B, they are not identical.
Law of Non-Contradiction: Either A or Not-A, an object or concept either is or isn't. It cannot be both opposites.
Law of Excluded Middle: A concept either has or does not have a property or distinction. A is A or Not-A it cannot be or.
Now apply this to gender.
Women and Men have certain distinctions that both don't share, Law of Identity.
Women and Men are opposites in those distinctions, so you can't be both (herms are infertile).
Those distinctions make you either man or woman, Law of Non-Contradiction.
Law of Excluded Middle, Man or Women no or aka NB.
Logic sound.