It begins with an entirely voluntary activity that some adults want to do—marry someone of the same sex. This increases their happiness without having any tangible negative impact on anyone else. It does, however, make many of the unaffected unhappy because they think it is a bad thing for those other people to do. There are a mix of reasons for this opposition, all of which are based entirely on a dislike either of certain kinds of people, or of the nature of their association with each other, or both.
Early in the same-sex marriage debate—the ancient faraway mid-’90s—the opponents felt no need to disguise this motivation. In language that later became an embarrassment to its defenders in court, the authors of the Defense of Marriage Act cited society’s right to express moral disapproval of homosexuality as part of its rationale. But as more and more of us shared our identity with our friends, relatives, co-workers, etc., our mundane reality undermined the prejudice. It became politically and intellectually unsustainable to prevent people from doing something solely because you were personally offended by it.
The argument then became that allowing people of the same-sex to marry would, in fact, harm people outside the marriage—that it would undermine social stability, and in ways no one ever coherently articulated, detract from conventional—i.e. opposite sex-unions.
At first these arguments were hard to counter.