Here's the down and dirty of it, and no I don't care to respond to those of you who will troll me for this post.
When it comes down to it, homosexuality is seen as some kind of malfunction or error because the sex drive is incongruent with the actual functions of the physical body parts. Gay man have the sexual attraction of hetero women, and gay women of hetero men.
"Sexy" Smells Different for Gay, Straight Men, Study Says
On an instinctive level, gay men are trying to impregnate other men and lesbian woman are trying to have the children of other women. This is why many traditional sources call homosexuality "confusion", as confusion doesn't always refer to your ability to reason.
It is felt by many that gay marriage, by extension, will be just as incongruent, that it will mirror the biological error compelling people to it.
Even if we went as far as to shake hands and agree that born-homosexuality were some kind of genetic error or deformity, so what? Other couples with genetic error or deformities are allowed to marry and they do just fine.
If it can be demonstrated that gays as a demographic are a high-risk-of-divorce group, just like mixed race and mixed religion couples are, then let's make it harder for anyone to marry with the same pen stroke we give gays "marriage".
The real problem is not who has what wrong with them, it's who can create relationships beneficial to society.