State has legitimate interest in preventing consanguination because it can lead to and propagate genetic diseases….
Incest often involves someone who can't give consent or is coerced into consent. State has an interest in preventing that.
Not all incestuous marriages would biologically produce children or not involve consent, so he has to use qualifiers like "often". But if we can withhold state recognition of incestuous marriage based on what would often result from those marriages, why can't we also distinguish between the opposite-sex relationship and the same-sex relationship based on the opposite-sex relationship's often biologically producing children? It seems to me that the common argument used by advocates of same-sex marriage - to the effect that biologically producing children can't be used to distinguish between the opposite-sex relationship and the same-sex relationship, because not all opposite-sex couples biologically produce children - is inconsistent with the arguments those same-sex marriage advocates commonly use against incestuous marriage. If opposite-sex relationships can only be defined by what's universally true of them, then shouldn't the same standard be applied to incestuous relationships? To be consistent, same-sex marriage advocates ought to abandon these arguments they've been using against incestuous marriage. On what grounds would they oppose incestuous marriage, then?
We base laws on generalities rather than universals in many contexts (what's generally the best speed limit for an area, etc.). From a practical standpoint, allowing all opposite-sex couples to marry is the most efficient way to handle the child-bearing issue. Elderly people sometimes have children, but usually don't. Since even elderly people have the potential to produce offspring, though usually only minimal potential, an efficient way to handle the child-bearing issue is to have the state recognize the marital relationship of all opposite-sex couples. It would be impractical to have the state doing things like giving people fertility tests to determine whether their relationship will be recognized by the state as a marriage. By contrast, there's nothing impractical about making the judgment that same-sex couples can't produce children. Even though elderly opposite-sex couples only have a minimal chance of producing offspring, that's still sufficient grounds on which to distinguish their relationship from a same-sex relationship.
Besides, biologically producing children isn't the only reason we have for distinguishing between opposite-sex and same-sex relationships. Opposite-sex relationships promote the unity of the genders in a way in which same-sex relationships can't, and we have good religious grounds for opposing same-sex relationships, for example. The child-bearing issue tends to get the most attention in these discussions, but it's not the only issue involved, and even that issue can't be dismissed as easily as same-sex marriage proponents suggest.