Neither do women who are done menstruating. So employers should hand out a questionnaire to all the women asking who still gets their period? I mean, that's a pretty normal question to ask your coworkers, I'm sure HR would be cool with it.

This is way, way easier to just implement as one extra sick day per person per month.

It's a tricky one, but on the whole I'm against 'positive' discrimination. It's still discrimination, it can still create contempt and undermine hard work (they're only in that job because they're [a], a smarter [b] probably didn't get the job, etc.)

It applies to maternity/paternity leave too. Until maternity and paternity leave are required to be equal by law, there will be a bias against hiring women, due to the simple mathematics. If the 'risk' is equal for a man or a woman, the bias is eliminated.

Even if men and women are given the same amount of leave, there are still two problems. First, social norms lead to men and women not using it equally. Second, single individuals don't have equal access given that society has a significant gender disparity in single parents, that men can't get pregnant, and that even if the leave is equal for adoption, there is still discrimination in adoption.

Neither do all woman.

They don't have to take the day off then.

The point is that they can still. Whatever the standard for taking time off work for illness it should apply equally to both genders so there should never be any need for a separate rule/law.

Because if you don't, it gives companies a reason to not hire women.

Employer: "Hmm... we have two candidates for the job, both equally qualified, but we'll have to give 12 extra days off a year to one of them but not the other. Which one do we hire?"

But there are number of health conditions that either gender can get that are rare and lead to many days of significant pain. Some even can result in bleeding similar to periods. Do we given these issues their own days off for those unlucky enough to have them? Or is it only counted in sick leave?

I feel that the workplace should attempt to accommodate any and all medical conditions.

Which tends to be accounted for in either general leave or more specialized sick leave. The idea of giving people more beyond this because of biological processes they cannot control raises the question of how we decide which biological processes deserve extra leave.