Well, overall I agree that the government has little or no business approving or disapproving or otherwise messing around with people's marriages.
But there is an argument in favor of such action, which stems from the presumed role of the government in regulating society, in this case providing encouragement or support to traditional (heterosexual, child-producing) marriages. This is of course because the continuation of our society requires it.
In general I don't like the government regulating private activity that doesn't interfere with normal functioning of society. I would be much happier overall if government simply was not in the marriage business at all. Marriage is the business of a religion, IMO. And that includes the Atheists as well -- if they wish to marry, great, have a party, whatever.
Unfortunately, from what I have observed, homosexual "marriages" are not very good at helping society continue smoothly. They are more prone to nasty breakups and infidelities than heterosexual marriages. And at the root, they cannot, by definition, produce children. Any children in a homosexual marriage necessarily came from a heterosexual relationship.
I feel great sadness for any child caught up in a nasty divorce. I can't imagine the awful confusion that would result from the additional burden of not being able to tell one unhappy parent from the other. Where are the role models, in such a mess??
The government doesn’t “regulate” marriage, it simply records the act and holds the participants to the contract accountable to the contract to the extent that children are involved. The participants have unlimited liberty to conduct the wedding and marriage however they see fit. No imposed regulation involved. No imposed renewal fee. No imposed training or proficiency testing required to be eligible. Simple.