I know this is "a very controversial subject," but what is the definition of marriage that these people are proposing that will include same-sex relations within it?

The only definition of marriage that I know of is the commitment between a man a woman, to give their lives to each other for their own good and to raise and educate their children... This commitment is an act of love... And their union is one of love...

The reason that civilization is interested in marriage (as an institution) is because the civilization is interested in the (1) well-being of its citizens, and (2) their offspring (future citizens).