"How does my same-sex marriage hurt your marriage?"
Glenn Stanton, Focus on the Family's Director of Social Research and Cultural Affairs (I love that job title!) gave it a whirl and what he came up with is that while he doesn't have a problem with individual same-sex couples marrying, he worries that blanketly allowing same-sex marriage will cause his children to think they aren't a necessary component of marriage. If his daughters see gay and bisexual men married to each other, they won't see the importance of a woman in a marriage and if his sons see lesbian and bisexual women married to each other, they won't feel they are needed in a marriage.
In reality, what he fears is that if his children see men married and women married, they might think being gay or bisexual is alright. If his children see that being gay or bisexual is okay, they may want wait twenty years in fear and self-loathing to come out. They might come out as kids or teenagers and embarrass him into leaving his job as a hatemonger.
And don't get me started about gender. He claims same-sex marriage will dilute the importance of gender in his children's eyes. Oh, the horror. They might not learn that female is only a function of and corollary to male. They might figure out that in the creation story, Adam and Eve were equally duped and equally punished by their God. They might realize that when man wrote "man" in the bible, God meant him to write "people." They might note that it was people their father who ensured that the Equal Rights Amendment to the United States Constitution was doomed. And if gender is so important, why do they claim otherwise when it comes to the rights and dignity of transgender people?