Because, if you oppose government interference in private life, the government should not be regulating who gets married. In fact, the government should be out of the marriage business in general. Stringent rules for child support are a legitimate government concern (according to real libertarians). Any church (in the broadest sense) should be able to declare people married. When confronted (having had this discussion with such little-l libertarians) with the “what do you do about women who gave up working and need post-marriage support” problem, such arguments tend to fall apart.
But the bottom line is that real libertarians (albeit with issues) are not the same thing as conservative. Or reactionaries. You can make such folk very uncomfortable by making this argument, as most are fundamentally homophobic at heart.