When debating about matrimony a lot of people bring up the sanctity of marriage, traditions or the need to progress. These are just fallacies, most of them ad antiquitatem and ad novitatem.
First of all, what is marriage? Marriage is a voluntary contract that make two or more people to share property, rights and obligations, like the responsability to rear their children. Therefore, the requirement of a valid marriage would be the consent of the parties, so both of them should be mentally sane and of legal age. Homosexuality is proven to not be a mental disorder by the Royal College of Psychiatrists, the American Psychiatric Association and the Chinese Society of Psychiatry, among other institutions.
At this point most libertarians assert the government shouldn’t intercede, letting individuals freely decide. However, we must remember one of the objetives of marriage: the responsability to rear the children. Kids need to be educated in a balanced and stable envirionment, where no spouse is superior to the other. According to the American Psychiatric Association and the American Academy of Pediatrics, it doesn’t matter the sexual orientation of the parents, as long as there are two. Poligamy is harmful because one of the members is de facto superior, while group marriage brings instability.
The conclusion is obvious: gay marriage and groupal marriage —not poligamy— should be legalised, but only married couples should be able to adopt children.