I'm aware of that. This is a case where one right is in conflict with another. There's no good answer. One group of people is going to lose and another is going to win.
The disadvantage women have is that they can't hide a pregnancy forever. Men can go to extreme lengths to hide their relationships. Although rare, it is not unheard of for a man to have two families at the same time, each one hidden from the other, and maintain this state of affairs for years before getting caught (otherwise we'd never hear about it).