Ok, so first off we want a secular justification of the claim that marriage has to do with reproduction. And secondly we want an explanation of how allowing SSM changes the definition of marriage. And thirdly, we want to see how changing this definition entails changing our understanding that children are best raised by their own biological parents. Let's see what we can do.
(1) How did marriage come about?
Let's assume a purely secular, atheistic, evolutionary worldview. How did we get the institution of marriage? Most animals don't mate for life, so why do humans do it?
The reason is because humans have a much longer maturation period than most animals. Most animals are mature adults within a year or two, and they don't need to learn a lot of stuff. What they need they can pick up from their mothers. They don't need a father around; his job is to spread his seed as far and wide as he can.
Humans are different. We take over a decade to grow to sexual maturity, and even longer to grow to social maturity. We are highly complex creatures that need nurturing over a long period of time in order to survive at all, let alone to survive well. We need the influences of male and female adults in order to develop as fully rounded individuals.
Evolutionarily, creatures will care most about their own offspring. Therefore, the people who have most interest in ensuring a child's survival and healthy development are the biological parents. In order to keep these interested individuals as the primary figures in the child's life for their whole developmental period, thereby ensuring the child's best chances of both surviving and prospering, the solution that makes most sense is for a male and a female to mate for life, producing all their children together in the same partnership, and living together in the same household as they raise their children and, later, help their children to raise their own children.
If marriage were primarily about the relationship of the two people getting married, there is no need to have such a binding social contract. They can partner for as long or as short a time as they feel they want to, and then move on, no problem. It is only the raising of children that requires the institution of marriage to exist. Moreover, the evolutionary reason for people falling in love in the first place is about reproduction - both having the children in the first place, and being committed enough to it to be willing to stick out the difficulties of living together with another person for decades.
This also explains why sex outside marriage (especially for women) has always been such a taboo. We know that children are best raised by their biological parents, and so society as a whole, and especially the men who are raising children, want to be very sure that the children that are being raised are the biological offspring of the parents who are raising them. It's pretty easy to know who the mother is, but harder to be sure about the father. So faithfulness in marriage is sacrosanct (especially for the women) for this reason.
This is further illustrated by the attitude to sex before marriage. In all cultures up until the latter 20th century, and in most of the world still today, couples who have sex before marriage are generally permitted if they are discreet about it (there is at least more leeway than with adultery), but if the woman gets pregnant then they are expected to marry. It is the raising of children that makes marriage important.
And even in today's society, where couples commonly live together before marriage, perhaps with multiple partners, probably the most common factor that triggers people taking the step of getting married rather than just living together is the desire to start a family.
I think that is enough to demonstrate the first point.
(2) SSM and the definition of marriage
So, in all cultures until recent times, and in most cultures still today, marriage is primarily about raising children. Of course, there are many things that go wrong in the actual world. A partner dies; the parents are not competent to raise their own children; the couple cannot live together harmoniously; a couple cannot have children naturally.
Within the framework of marriage, these things can be worked around to make a less-than-ideal but best-of-a-bad-job solution. We make provision for adoptions of children by non-biological parents. Many, perhaps most, adoptions work out really well, and the children and parents love each other. But they still recognise that this was second best. The children want to know who their 'real' parents were, and, if the clock could be turned back and the biological parents were able to look after the child just as well as the adoptive parents had been, we all feel that would have been a better solution. The adoptive parents love their children very much, but if they hadn't suffered from infertility then they would really have preferred to raise their own biological children. (Others may adopt additional children after they have had some of their own, in order to share their good fortune with others who are not so fortunate. But very very few people who are able to have children of their own choose to adopt instead of having their own biological children.)
We also allow remarriages, so that some children have step-parents. But in the re-marriages, the couple getting married will also very often want to have children of their own within that marriage. Even if the remarriage takes place when they have passed child-bearing age, if they could have had children together they would probably have wanted to. We also recognise that step-families are never an ideal situation.
We also support single parents, but we know that statistically children from single-parent backgrounds will face an uphill struggle to prosper as compared with children raised by their biological parents in two parent families.
However, in nearly all cases of marriage, there is a desire for the two people involved to have and raise children together. Sometimes this is not possible because of infertility, old age, the prior existence of other children making it practically difficult to have more, and so on. These are all recognised as non-ideal situations, but they fit within the principle that marriage exists for the procreation and rearing of children. This is the reason that marriage came to exist in the first place, and marriages take place between two people who, all things being ideal, would be able to reproduce and raise a family. Because of this ideal, we allow marriages even if the ideal cannot be realised. (However, as noted before, if the need was only for the two people involved to have companionship, the institution of marriage would never have evolved.)
However, with SSM, the two partners getting married, even in the most ideal of circumstances, cannot possibly procreate in order to be able to raise their biological children together. They are entering a partnership that is designed for the rearing of children by their two biological parents, but are unable, even in the ideal situation, to do so.
I think there are very good arguments in modern society for allowing what in the UK we called 'civil partnerships', which allow all the rights of marriage as are needed for companionship, but stop short of calling it marriage. When civil partnerships were introduced in the UK, it was said that gay marriage wasn't needed and wasn't just around the corner. And the reason for having civil partnerships rather than gay marriage was because it was recognised that marriage is about having children.
By calling homosexual partnerships 'marriage', however, you are saying that they are the same kind of thing as a heterosexual marriage. In order to make this claim, you need to redefine what marriage is understood to be about. It is no longer about raising children; it is about the love of the two people getting married.
3) Who is best at raising children?
Moreover, if all people who are married are to be regarded as having the same status, then differences with regard to the ability to have children need to be removed. We therefore need to get rid of the belief that children are best raised by their two biological parents, and say instead that any two competent adults are just as good at raising children.
So there are two very important changes that have been made:
a) marriage is for raising children -> marriage is about the love of the partners for each other;
b) children are best raised by their two biological parents -> any competent pair of adults is just as good as the biological parents to raise a child.
Now, from a purely secular point of view, if society wants to make such changes to the way it thinks, it can't be stopped from doing so, since there is no moral absolute. But if we are making such a change, it is disingenuous to pretend that no change is being made; rather one should acknowledge the scale of the change that is being made. Moreover, the people should be properly informed about the nature of these changes and properly consulted about whether they really want to make these changes. At least in the UK, that has not happened at all. With regard to the second change in particular, I am pretty sure that most people do not believe that, and would oppose that view if they realised that that is the implication of allowing SSM (rather than just civil partnerships).
Actually, if we really believe that any two competent adults (or, indeed, why does it have to be two? why not one, or three, or seven? but that's a whole nother topic) are just as good as the biological parents at raising children, we actually should take this further, because there are plainly many biological parents who don't do a great job, and many people who can't have children who might raise children quite well. So what we should actually do is have people sit a parenting competency test to judge whether they are going to be good parents. Any children born should immediately be removed from their biological parents, and given to the couple with the highest score on the parenting test (who haven't yet been given a child). That would make society a whole lot better, and everyone would be happy. It's discriminatory against people's right to have a child if they are deprived simply because they are not biologically capable of having one. So this would be the fairest thing all round.
(Do you know what? I started that last paragraph as a joke, but I'm now seriously worried that some people will actually think it's a good idea...)
'Nuff said.
Roonwit