The only other way I can explain this is that to project population, all you need to know is the the number of women now and the rate at which women are giving

The only other way I can explain this is that to project population, all you need to know is the the number of women now and the rate at which women are giving birth (assuming births are 50/50 male/female). At least, those are the more direct parameters to use than the number of men or the rate at which men impregnate women.