We set several limits on who can get married, the main one I can think of right now is a minimum age. I think it's 16 in California. The reason for that is rational, having to do with a concept of informed consent. But whatever the limits of who can marry whom are, they have to be rational. It would not, for example, be rational to prohibit a Latino from marrying a black or a left-hander from marrying a right-hander.
We also prohibit siblings (cousins too) from marrying each other, the rational basis for that being the health of the children that might arise from this marriage. Second cousins are ok, not sure about aunts or uncles. Parent-child marriages are a no-go.
I have yet to hear a rational argument against same sex marriage. The strongest argument I've heard is that's always been so, so it must always be so. But surely if a rational argument existed, it must be stronger than the "it has been thus, thus so it must always be".
An interesting gotcha argument by the right-wing would be asking why an incestuous gay marriage should be prohibited, since there is no chance of an offspring arising from a same sex marriage between a dad and his son. I'd have to work out an argument for that, but there is no question in my mind that incestuous marriages of any kind, same or opposite sex, must remain off limits.