I think you are actually arguing against your own point, Lars. You use the term "assigned," as in being assigned a sex category at a certain biological point of the development of a fetus. The assignment of a category is a social act, not a biological fact. The assignment and use of pronouns is also a social act. Even science itself is social in that we, as a society, have determined some scientific facts to mean something in the social sense. For example, that the shape of a person's genitals has any social significance at all.