These comments pertained to transgender men (i.e. biological women who identify as men) and the matter of whether or not only women can menstruate. Rowling declared her belief that this is the case ("People Who Can Menstruate").
Of course, from a biological standpoint, it is true that only women menstruate. Men do not. The only possible dispute one might make is in the case of those who are intersex, born with some degree of both male and female anatomy. However, even then, menstruation is recognized as a biological female attribute that the person has (part of what defines them as intersex), not a unisex one (like having eyes or a spinal cord).
The reason this is of any controversy at all is because transgender men consider themselves to be men, yet have female bodies that still perform the functions of female bodies (especially early on in the gender transition process). This means that there are people who menstruate (and occasionally even bear children) who identify as men.
This, of course, raises one of the most enormous worldview and societal questions of our time (at least in western society): is gender determined by biological sex or not?
