When I was 15 I considered myself a devout Christian and was opposed to gay marriage. I felt it did take something away from the institution of marriage, even if it didn't effect me directly, because I believed what I was told that acting on homosexual impulse was a sin. I also had an understanding of the world filtered almost entirely through my understanding of scripture and my faith, and in that world-view the Bible is the basis for all morality and marriage is a sacred pact originally engineered by God Himself between Adam and Eve. I saw gay marriage as a perversion of that and an affront to this tradition.
Even then, as now, it still galled me how many that called themselves Christians were so selectively concerned about THIS particular affront to their faith. Divorce, fornication, pre-marital and extra-marital sex all bothered me just as much as homosexuality did, no more and no less. I noticed the hypocrisy in other "Christians" who savagely denounced gays and how they damaged the institution of marriage without giving near as much attention to these other things.
Then, as now, I was very reluctant to pass judgment on anyone else. I understood that to be God's job, not my own. It saddened me to see so much sin in the world, so it did actually effect me personally, but what bothered me more was the hate speech spewed by those who proclaimed themselves Christian, directed at other "sinners" when they themselves were acting in very non-Christian ways.
For these and a thousand other reasons, I eventually lost my faith. I consider myself a recovering Christian now, since even though it took me a long time to get here, I'm much happier and more well-adjusted than I used to be. I'm probably much quicker to pass judgment now than I was in high school, and far harsher and more outspoken in my criticism of others, but my attitudes and beliefs regarding human sexuality, the human condition, and "victimless sins" have changed drastically, and now I tend to think that I get upset for more of the right reasons and fewer misguided ones.
I don't have much use for tradition or convention anymore, and I no longer believe that the sole function of marriage should be to raise god-fearing children. Because of that, I have no other way of reasoning that gays should not be allowed to marry if they want to. It makes them happy, and doesn't upset anybody other than those who are overly concerned about how other people live their lives. If the traditional definition of marriage has to be changed to accommodate this, I don't think that's a bad thing. Lots of things change and nobody bats an eyelash. When there is resistance to change, more often than not bigotry, misguided fear, or a lack of understanding is the chief culprit. I don't think any of these things are good reasons to preserve tradition.