In 1971, the Minnesota Supreme Court ruled, in Baker v. Nelson, that (1) the state’s marriage law does not authorize two men (or two women) to marry each other and (2) the law does not violate the United States Constitution. See here for the text of the opinion. I lectured on this case in my Sex, Ethics, and the Law course 20 years ago (at the University of Arizona). It’s interesting that the court addressed the argument, which is now often heard, that if (i.e., since) the purpose of marriage is procreation, heterosexual couples who can’t procreate should not be allowed to marry. The court wrote:

The equal protection clause of the Fourteenth Amendment, like the due process clause, is not offended by the state’s classification of persons authorized to marry. There is no irrational or invidious discrimination. Petitioners note that the state does not impose upon heterosexual married couples a condition that they have a proved capacity or declared willingness to procreate, posing a rhetorical demand that this court must read such condition into the statute if same-sex marriages are to be prohibited. Even assuming that such a condition would be neither unrealistic nor offensive under the Griswold rationale, the classification is no more than theoretically imperfect. We are reminded, however, that “abstract symmetry” is not demanded by the Fourteenth Amendment.

This is exactly right. Law is not morality. It deals with classes, not individuals. Homosexual couples cannot procreate. Heterosexual couples can. That is the difference that makes the difference.