The problem most rational people have with gay marriage is that it has and will continue to tread dangerously on religious rights. This was initially washed away as a "slippery-slope" or "fear-mongering" argument, but nobody can deny many of them haven't come to fruition.
First and foremost is that a morally grounded society cannot encourage or facilitate homosexuality. The medical data is clear on this. It's a dangerously unhealthy lifestyle for the individual and carries a high risk of depression, STD, HIV, among other things. To counter the usual explanation for this, there is no clear link between treatment of gays and overall mental health of said gays (otherwise, gays in ultra-liberal places would in a constant state of euphoria given how much homosexuality is glorified in these places). To add to this, there is the tendency of gay individuals to act in a very certain way (upright posture, strutting buttock, forced accent and lisp etc), as well as for gay couples to often delegate the role of dedicated male and female among each partner, indicating that there is more here than simply a sexual orientation. Homosexuality is a state of confusion and embodiment of mental tendencies which should be addressed and controlled, not celebrated.
Further, the bigger issue with this is that almost all major religions (which, like it or not are here to stay) condemn homosexuality. Followers of said religions should have the right to uphold these religious beliefs. That means if I choose not to take part in a gay wedding, the government should not be able to force me to do so, anymore than the government cannot force an atheist to attend mass or a Muslim to eat pork. That's a violation of religious freedom. So while I don't directly have a problem with what gays do in their own personal lives, I do have a problem when they try to destroy my livelihood because what I do in my own personal life. What ever happened to live and let live or tolerance, the staples of the gay movement? They went out the window as soon as gays gained a voice.
Then there's the issue of gay adoption, which is clear-cut child abuse. Should I pass away tomorrow and have nobody but the State to care for my children, I should have the right to mandate that my kids, born of a religious bond between a man and a woman, are not put into the care of a gay couple. Given the blatantly extreme hostility the gay movement has taken against religious people and their views, you cannot convince me that a gay couple would accept my 12 year old religious son. They would convince him that his views are wrong and that there's something wrong with him and needs to change, which ironically is the exact same thing gays have claimed makes them depressed when their own family does.
All of these moral dilemmas, which clearly impede on the rights of religious people, have been destroyed in favour of glorifying homosexuality. Excuse my willingness to think that more of my rights will be impeded as gays continue to dominate the mainstream political spaces. When the government has resorted to holding Christian businesses at gunpoint to make a gay marriage their business, I have little faith left that this movement has anything to do with love, tolerance, acceptance, diversity, or any of the other words adopted by the gay movement.
