Define what a girl is then. There are plenty of women born with an XY chromosome defect that would biologically make them male. But they live and present themselves as female. Would you refer to them as men, then, because it is an undeniable fact that they are? What of those who are born interlove? Do you require female loveual organs to be a woman? So then what becomes of the women who have hysterectomies, or other defects with their ovaries/uterus/whatever that causes them to be removed? Does it just take a vagina and breasts to be a woman?
You're perfectly allowed to think that love and gender are black and white, but they really aren't.