> Whether a person is male or female depends on exactly one thing: their chromosomes.
That is (mostly) true, but "male" and "female" are sexes, not genders. One's gender is more correctly referred to as "masculine" or "feminine", and while there is a general correlation, the two categories do not always correspond. One's sex is a biological concept, but gender is a social/cultural phenomenon. Quite a few things which do not have a biological sex--and perhaps are not even biological in origin--are still considered either masculine or feminine. Just look at languages like French and Spanish, where all nouns are assigned a specific gender. Even in English there are a few cases like that; ships are always treated as feminine, for example.