Since I live in the US, and the current debate going on in this country, it is what I'm most familiar with. But sure, go ahead and talk about any country you want.
Thanks for the clarification. The legal issues, social norms and historic background are all quite dependent upon location, so there might be differences between a generalised treatment of same-sex marriage as a concept, and it's application in a specific area.
Reasons I can think of that a non religious person would have issue with gay marriage.
1) It makes a mockery of traditional marriage:
In western cultures, marriage has been a one man-one woman affair for a VERY long time. Sort of what I think was previously suggested in this thread, a lot of people may find it sad to see a deeply ingrained social convention being tossed aside and replaced with something new with the same name.
2) It's a slippery slope that will lead to ridiculous unions such as men marrying their dogs:
The slippery slope is often held to be a fallacious way to argue. But I will mention how the same-sex marriage issue went over here in Finland. At first, they were asking for nothing more except registered partnerships. They got it. Then they began asking for nothing more except in-family adoption. They got that, too. Then they asked for nothing more except out-of-family adoption. Yup, they are getting it too. Now they are asking for nothing more except gender-neutral marriage.
With this kind of history, one might be rather hasty to believe that this will be the end of it. The end of what, you ask, what more is there after same-sex marriage has been legalised? Well, why stop with gender? According to my interpretation, many of the same reasons given in favor of same-sex marriage are equally applicable to several other persuasions as well, and it might be just a matter of time until they begin clamouring for equal rights and recognition.
Legally speaking, is marriage a natural right of all humans, or is it a legal right and a contractual matter? Both definitions may present some problems. Contractual issues can and are being regulated by the government for the public good by due legal process. This would place the question of same-sex marriage within the jurisdiction of the legislature, and the will of the majority which is subject to change. If marriage is a natural right in which the state has the authority to intervene only in cases of overriding public interest, then would it be possible to marry close family members, or all of them for that matter. Inbreeding is possible only in cases involving reproductively viable individuals of the opposite sexes. If mutual consent and no harm to others are the only guiding principles, which I believe is the position advocated by most same-sex marriage proponents, then how could such a union as that be prevented while maintaining consistency and fair and equal treatment? Or is it something seen as permissible under the new system?