There simply is no rational argument for disallowing marriage to someone of the same gender. Superstitious reasons exist, but these aren't rational reasons and, thus, are not valid. Marriage is a secular process and social construct that has been perverted and exploited by religious cults in order to ensure the survival of the individual cult. This much is clear in both the archaeological and historical records and (only the truly ignorant maintain that marriage is solely a religious construct).
The argument that allowing same sex partners to marry is akin to pedophilia is ignorant and irrational fallacy meant only to malign and argue ad hominem with a straw man rather than to demonstrate a rational reason for disallowing same-sex marriage. One does not permit or allow the other and only the ignorant or the disingenuous would maintain such a position.