Well just to point out my first comment was completely a joke in case anyone didn't follow that. While I don't think there are sexist reasons that we don't have men's hospitals I do think that in the end, regardless of our reasons for not having them, it is sexist.
We can all sit here and say that the female body is more complicated, and there are reproductive issues and maternity issues to justify why there are women's hospitals and not men's hospitals but that is just ridiculous. The fact is there are diseases and conditions that ONLY apply to men, which women will never have and cannot have. Why do they not deserve specialist to work with them on those specific issues?
The fact is most of society still see men as the norm, the people who are (or were) in control, the people who ALREADY have access to everything... so why do they need "special" treatment? (not using the word treatment to mean health treatment by the way) So many people already see things like same sex marriage as special treatment, hate crime laws as special treatment, blah blah. We all know that list goes on and that is isn't really asking for something "special" it is asking to be allowed to become equal.
Today while there are still plenty of things that men have easier access to there are lots of everyday things we never even pay attention to them NOT having access to. Some examples would be child custody in divorce cases, it almost always turns out the mother will have primary care of the children rather or not either parents in unfit. In fact in most cases the father has to go out of his way to prove the mother unfit if he wants custody, but he does not have to be proven to be an unfit parents for the mother go get custody. And I do say this from several cases that I have seen first hand. It is a fact rather we like it or not. Men have a harder time with cases of rape or abuse as well, because most societies see it as unreal or unlikely that a man could be a victim to a woman. While it is LESS likely, it is still very possible and has happened. In fact we have tons of studies and research that shows it probably happens much more than anyone would believe but men don't even come forward about it. And why would they? We all say they are afraid of being less masculine or seen as weak... in the end though what's the point in coming forward when they won't be believed?
I'm not saying men have it horribly, but we often ignore that they are victims of sexism or that they need access to things that we often take for granted that we should be allowed. We assume they have a level of access we don't have. There is very little awareness amongst men of the possible health problems they face, they rarely go to doctors... there is no push against this currently. No big campaign (at least not in my area) to get men to be more active in their health. There is no push for education for men on their health issues in general, but there is a huge push for females to be aware and to get checked. We do push on a few subjects for men, but only one or two, and even then we don't push nearly as hard as we do for women.
So in the end it is something that is sexist about our culture, we just don't recognize it as often because it is hard for us to see and accept that men are also victims of sexism. We tend to reserve that word for women. It may be different in other areas or countries, I wouldn't really know about that obviously so I am speaking mostly about American culture.