Sorry, I missed this before. I'll try and expand.
Marriage, marriage laws, and also marriage customs (which in some places are what govern marriage rather than bureaucracy as with our system) are big picture things. They exist in society largely as a way to address the results of procreation, and also inherent disparities that happen between the sexes in marriage. It provides some benefit to individuals, but even more, it's about the benefit to society of creating customary or legal obligations between parents of children.
The question of individuals being fertile or infertile isn't really something that is usually queried directly, it's assumed that most people are fertile, and that the rules will be effective in the main. It's also going to be quite impractical, or even impossible historically, to guess who will be infertile - it would require a lot of effort for little benefit. (That being said there have certainly been societies/times where infertility or impotence is grounds to dissolve a marriage.)
It's only quite recently that it became possible to easily avoid having children while sexually active. It's not been a very common circumstance historically.
Anyway, the main issue here is about how the law sees sex, or reproductive role. There are people who argue that the reason that it is wrong not to recognize SSM is that it is discrimination on the basis of sex - that there can be no recognition of sex by the state as a legitimate legal category. As legal entities, they feel, we are all effectively neuter.
Now, I think this is not clearly legally true in the UK, but it does for example seem to be true in some other places where SSM laws were changed by the courts, and there are lots of people who think that way even in the UK, and extrapolate it to other areas.
Mainly these are people who have accepted that sex does not significant affect on people's lives, or at least that it shouldn't and when it does it's because of sexism and should be stamped out. They believe that in an ideal world without sexism there would be no real difference between men and women apart from genitalia. (This idea is by a long way more common on the left, among progressives.) If bodies aren't important in our lives, they don't need to be important in our social institutions, or laws.
Another way to think about it is around the idea you mentioned - even if marriage exists mainly as a cultural way to manage sexual reproduction, what difference does it make to include ss couples? It would still do that, just as when it happens to include infertile couples.
That's certainly possible, but it still leaves the possibility of defining situations where sex is important to certain institutions or customs. If we've said it's sexual discrimination to differentiate at all, that's going to mean there will be no situations where it's acceptable.
I feel like this is a bit rambling, I hope it clarifies what I mean a bit.
Really, I think part of the issue with this is the liberal left tended to see it as a question of individuals rights. Whereas conservatives say it as a social-institutional question about how to structure male-female relations. They tend to talk past each other as a result.