The rest of your argument around mutual care is reasonable. There are more nuanced views than a blunt "if state support for marriage depends on procreation, let's ban marriage for infertile people as well.", which sounds like spite: if I can't get it, then those guys over there should not get it either because they are similar to me on dimension X.
From the perspective of the state, there is a man, there is a woman, statistically they have a high probability of having and rearing children. Splitting hairs whether they are fertile / infertile is something the state shouldn't get into, partly because it's administrative hell and partly because it's an invasion of privacy.
With gay marriage, there is a man, there is a man, statistically they have close to zero probability of having children, so from the perspective of perpetuating the state, there is no statistically significant benefit in offering them special treatment.
We can now argue whether the state has the right to determine the gender of an individual, or whether that's an invasion of privacy as well. It's pretty easy to tell a man from a woman at birth. Biology and cultural norms make this distinction pretty obvious to anyone who's paying attention. It's both cheap and reasonable to tell apart men from women.
The decades and decades of non-consensual infant "corrective" surgery of people with intersex conditions, leading to physical and mental damage (and in some cases involuntary sterilisation), suggests otherwise...
http://www.theatlantic.com/health/archive/2014/07/should-we-...
http://www.independent.co.uk/news/uk/home-news/special-repor...
You're just trying to rationalize your prejudice by pretending it's about fertility.
PS. I'm a parent, thank you very much.
So, you think marriage shouldn't be available for straight people who are both infertile?
You ignore the important role that marriage plays in mutual care. Marriage gives legal backing and support (in the form of certain tax and other financial and non-financial benefits) to a reasonably large set of people in long-term care relationships. Those people who care for each other aren't going to be needing as much support from the public purse to care for them when they get older, because they care for each other.
My dear old grandparents cared for each other when they were old - when my grandma died, my grandfather had to go into a residential care home. But because they were together, they provided care for each other that prevented both from needing that social care for a long time. Long term gay couples will give something back in return: caring for each other, providing health and wellness benefits that would otherwise be something that the welfare state may need to provide.
The state has a strong vested interest in people caring for each other. Here in Britain, the support given to parenting are done for parenting regardless of marital status in the form of child benefit payments.