Fr. Federico Lombardi, Director of the Vatican Television Centre, has invoked the dreaded slippery slope argument against legalized gay marriage:
In short, preserving a vision of the human person and of human relationships where there is a public acknowledgement of monogamous marriage between a man and woman is an achievement of civilization. If not, why not contemplate also freely chosen polygamy and, of course, not to discriminate, polyandry?
Rather than dissect the problems with this line of reasoning (which Jay Michaelson, the writer of the linked article, does much better than I could), I will simply say, “Yes, why not?”
This is the libertarian me talking, but the government has no business being involved in marriage at all. Let the state authorize contractual civil unions if it finds a compelling reason to do so, but validating or enforcing types of relationships is just a way for the government to insert itself unwarrantably into our private lives.
Also, polygamy is not the opposite of polyandry, polygyny is. Polygamy is a gender-neutral word. Words matter.