"Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh." - Genesis 2:24
Genesis means beginning, and it is significant that in the very beginning God brings a helper suitable for man. It is significant that the helper he found for him was not another man, but a woman. Woman was taken out of man to be his other half. So on Genesis alone we have our reason for being against same-sex "marriage." Why? Because it isn't marriage as God defined it to be. I don't even need to share Romans 1 with people to prove homosexual activity is wrong, although I do because it so clearly shows that we Christians are not homophobic gay-haters, but have learned from our God the sinfulness of it so we side with God's opinion.
God's opinion started with the creation of man, then woman. He made a beautiful order and combination. We find in Ephesians that it was ultimately made by God to be a picture of Christ and the church. Same-sex "marriage" takes this beautiful mystery and gets it mixed up. The relationship marriage was meant to portray was not Christ and Christ, or the church and the church, but Christ and the church! Those who try to say they are Christians and totally in support of gay relationships, fail to acknowledge that the Bible doesn't say anything in support of gay marriage, only the opposite. Hebrews tells us to "keep the marriage bed holy." Holy means set apart. No sex outside of marriage, including that which is called "marriage" but is not really marriage.
To finish, I understand that someone who doesn't believe the Bible has no reason to side against same-sex marriage. With the view that we are all just beasts like all of the other animals in the world, I can see why there's no moral objection. Although, I can also then see why there is no moral objection to anything anymore. I can think of two polls that compared people's care of human strangers over their own dogs lives, and it found that 40% of people would save their dog over a person. Without God, moral standards start to decline, lines start to get blurred, and people start to think that human law is the only objective right and wrong. It doesn't matter, there is still the Most Supreme Court in heaven where God judges the justness of every single thought and action of man. He, the inventor of marriage, has clearly defined it to be between a man and a woman.