Douthat’s point, basically, is that the marriage norm has continued to erode, across the West, even as the movement for same-sex marriage has burgeoned. Hence, one might plausibly argue that the movement for same-sex marriage, which, in his words, “press[ed] the case that modern marriage has nothing to do with the way human beings reproduce themselves, that the procreative understanding of the institution was founded entirely on prejudice, and that the shift away from a male-female marital ideal is analogous to the end of segregation” was a contributor to that trend away from a marital norm, or at least had a common cause with whatever forces were driving that trend. As such, he calls for liberals to be magnanimous, recognize trade-offs, and say that this trade-off was worth it.
I’m all in favor of recognizing trade-offs, and that all good things don’t go together, but I think to do it right you need to look deeper, and not pick one (still somewhat) controversial proposition and highlight it for that kind of analysis. The deep causes of the decline of the marriage norm are the rise of the equality of women and the yawning wage gap between the working classes and the profession and upper-middle classes. Marriage has become aspirational rather than normative because men are less-desireable than they used to be, both because women need them less and because men can offer less than they used to… And once a bunch of people fall off the path more or less voluntarily, cultural norms change. They take time to change, but eventually they reach a tipping point where they can no longer be called norms.
So the trade-off is not “was gay marriage worth the cost to the marriage norm” but “was giving women the vote worth the eventual cost to the marriage norm.” And that’s a question that’s almost impossible to grapple with, because it’s impossible for us to look at the question in other than historical terms. As Matt Yglesias points out, the counter-factual with respect to gay marriage is not “what if this movement had never happened” but “what if the balance of power had tipped the other way for longer.”