Actually, the woman's vaginal environment can kill of X and Y sperm, so it isn't all male-dominated. Plus the woman's body can spontaneously abort a male/female foetus: this often happens before the period is even late, so most people who have this assume they're either a day late or that they didn't conceive that month. Only with early HPTs are more of these cases coming to light.

Men have both X and Y sperm, they don't make more of one sort, although men can also kill off one sort or another before they let them loose on the world.