We all agree that God’s intended way of procreating and raising offspring was through the flesh of a man and a woman. That is the spiritual basis which Christians use to oppose same sex marriage. This may also be true across other religions.
There are many non-believers who do not profess Christianity or other religions or people who have little faith in Christianity or in other religions. Yet, these people greatly oppose same sex marriage. Of course, the reasoning of such people is not based on only religions teachings.
Non-religions reasons for opposing same sex marriage.
sodomy is sinToday, if you are told, for instance, to design a system, may be a prototype, or a cheat which will outline how children will be raised well, in a disciplined manner and in an environment where they are able to enjoy all their rights & freedoms and where they are provided with all the needs which pertain to healthy children, then you’ll find the system you come up with include a mother& a father. There could be others, of course, but the above system is the most ideal to provide children with all the love, support and care they require as they grow.
Also the fact that there is biological connection between children & parent proves the logic that be children will be at a better position of identifying themselves with their parents and naturally the parents will be at a position to sacrifice all at the disposal (mental, physical and emotional) so that the children are successfully raised to be responsible in the society.
Some of the arguments against same-sex marriage which don’t have religions grounds include:

Children will mostly hunger much for biological parents.
In same-sex marriages, lesbians will be the most likely couples to have kids, than gays. These kids would love to be identified by their fathers and mothers and will certainly need to know whom they are. Also in most cases, children always need to know more about their parents. This interprets that they feel more secure being with biological parents.

There is fear that children raised by homosexual parents may have problems with gender and sexual orientation.
There is fear that same-sex marriage would lead to the rise of infidelity in marriages and also weaken the structure of marriage in the event that the matrimonial union between the couples is severed.
Parenting of same-sex marriage maybe inadequate to kids in the event that the child needs a father who absent among lesbians or a mother absent among gays.

Sexually transmitted diseases are found to be on the rise among same-sex communities hence a lot of opposition.