Thesis: Marriage as a natural kind of relationships is a better theory than marriage as an institution defined by socially instituted rights and responsibilities.
Argument 1: On the institution view, we have to say that people in most other cultures aren't married since they don't have the same socially instituted rights and responsibilities. That's bad, since they say they're married when they learn English. The natural kind view holds, instead, that people in different cultures are referring to the same kind of relationship, but may get wrong what is and is not a part of the relationship.
We do not automatically accept educational credentials from other cultures. Thus, being medically educated in France does not automatically make one count as medically educated in the U.S. And being medically educated in 5th century France would make one not one whit medically educated in 21st century France (imagine a 5th century doctor who travels in time). In other words, being medically educated is always indexed to a set of standards. But we don't think of marriage in this way, with a few notable exceptions, such as polygamy or same-sex marriage. Getting married in India is sufficient for being married in France. Why? If one thinks of getting married as assenting to a set of rights and responsibilities, then getting married in India shouldn't be sufficient for being married in France, or vice versa.
Argument 2: The natural kind view explains how we can individually and as a society discover new rights and responsibilities involved in marriage. The institution view leads either to constant abolishment of the old institution and replacement with a new one, or to a stale conservatism. We learn about the rights and responsibilities of marriage experientially and not just a priori or by poring over legal tomes. That is how it is with a natural kind like water.
Argument 3: Suppose we see someone from a patriarchal culture who is failing to care for his sick wife (or at least someone he calls a wife). We might well say: "It's your duty as a husband to take care of her." On the institution view, he can respond: "No, it isn't. It would be my duty to take care of her if I were her husband-per-American-rules, but I am her husband-per-Patriland-rules, and in Patriland wives take care of their husbands and husbands do not need to take care of their wives." But on the natural kind view, we can say: "You tried to marry her, and marriage does require taking care of a sick spouse, regardless of who is of what sex. So either you succeeded at marrying, in which case you have this responsibility, or you failed at marrying, in which case you don't have the rights you thought you gained." On the institution view all we can say is: "You're in a corrupt and sexist institution, and you should divorce to stop supporting it. By the way, you're right that you have no role duty to take care of her."
Argument 4a (for conservatives): If you take the institution view, you play into Wedgwood's argument for same-sex "marriage".
Argument 4b (for liberals): If you take the institution view, you cannot advocate same-sex marriage, but only same-sex "marriage". You have to adopt the very revisionery position that marriage should be abolished, albeit replaced with something very much like it, namely marriage*, since marriage is defined by the social understanding, and that has included opposition of sexes. Moreover, such a view leads to unhappy consequences. Once we have replaced marriage with marriage*, we can't say that our grandparents are married*, only that they are married, and since marriage* is the only relationship available after the revision, you can't do what your grandparents did. Moreover, even allowing our grandparents to stay married is problematic if marriage is an unjust institution. So probably the state needs to dissolve their marriage, leaving it up to them whether to marry*. This is a politically untenable and unhappy view. A much better view is that marriage is a natural kind, and we were simply wrong in thinking marriage is only for people of the opposite sex. This (and Argument 3, too) is a species of the general point that relativistic theses run the danger of leading to stale conservatism.