I think it just comes down to morality. I couldn't think of any logical reason for each side's position other than that. Some people would say that you shouldn't impose your morality onto others, but I think that that overlooks the point that every single law is based on morality. Somewhere, people got together and decided that murdering someone is morally wrong, so it should be punished. And embezzling money from a corporation is morally wrong, so that should be punished. All laws are morality-based.
But I have to wonder if a constitutional amendment is really necessary. Thousands of amendments have been proposed over times, but only a few have ever been ratified, and that indicates that amending the constitution should only be done in serious cases for serious issues. State legislatures or Congress could just make laws banning gay marriage.
However, just about every single time a state passes a ban on gay marriage, some judge somewhere overturns it on the basis of one ground or another. Louisiana passed a gay marriage ban by almost 80%, and a couple weeks later, a judge ruled it unconstitutional. And in Massachusetts, their supreme court ordered the legislatures to pass a law legalizing gay marriage
by a certain date. The courts are so out of whack to their constitutional obligations that I think the only benefit to having an amendment to ban gay marriage would be to keep judges from imposing their own personal beliefs and overruling the will of the people.