The speaker has an ideological vision of what the society should look like, and in particular, what the government-dictated universal terms of marriage should be (both with regards to the institution of marriage itself and its tremendous implications on all the other social institutions). He uses the libertarian argument because its implications happen to coincide with his ideological position in this particular situation, but he would never accept a libertarian argument in any other situation in which it would imply something disfavored by his ideology.