If you let gays marry, then you will have to allow polygamous, incestuous, or inter-species marriage.
Clearly, with laws already saying that marriage can only be between one man and one woman, it is possible to craft marriage laws that still exclude more than two people, those who are blood related, and animals. So there is something else going on here.
One part of that something else is the "slippery slope" -- if you allow one thing you don't like you have to allow other things you don't like.
Gays aren't helping the issue by saying, "You should be able to marry the person you love." Then you have to argue why gay marriage is different from polygamy and the rest. We have restrictions on marriage and we need good reasons why those restrictions should have exceptions, since those restrictions are for the good of the society. If I understand it right, we don't let siblings marry because of the higher chance of genetically deformed offspring -- meaning the possibility for procreation and its effects on society are a part of the definition of marriage.
Gays could say that we marry for love within the several agreed upon and important criteria. That is unwieldy (and no sound bites) and it makes me wonder where on the web I might find a master list of the agreed-upon criteria of the definition of marriage (love, no coercion, of legal age, etc.).
So how to combat the original argument? Devil's advocate?
What's wrong with polygamy? If marriage is about procreation, then polygamy is efficient. It even handles the impression that men tend towards promiscuity. So the straight definition of marriage, not the gay, supports polygamy. Besides, isn't the reason why polygamy is outlawed is because Christian sexual morality disapproves of it (which makes me wonder what part of the Bible gets quoted here because the Old Testament is full of men with multiple wives). Come to think of it, Christian sexual morality disapproves of gays with as much evidence.
Incest? Gays don't have kids through natural means, so it isn't possible to pass on genetic deformities. Big difference between the two.
Inter-species? Ridiculous. Animals cannot consent to marriage.
So back to the idea that we need to keep marriage strong and allowing gays to marry will cause the deterioration of the institution. Actually, that claim is exactly backwards -- preventing gays from marrying leads to the deterioration of the institution. There is lots of study on this point but the clearest answer is Massachusetts. The state has close to the lowest divorce rate and since gay marriage was legalized the rate has dropped. There is also little evidence for a demand in polygamy, incest, or inter-species marriage. We'll let those who demand it to make their own case for it. Society can decide these things separately.
So it all comes down to Christian sexual morality approves only of marriage for one man and one woman and all else is banned. What this is about is challenging the Christian hold on sexual morality. It is also about whether the state has a compelling reason to deny gay marriage. And saying, "Well, if we let gays…" isn't compelling.