Libertarianism has, snce its founding, been a melding of two strands of thought.
1. MORAL: your preferences do not constitute a reason to send people with guns to shoot folks who disagree...except if the other guys are using guns against you.
2. PRACTICAL: governments suck at, and generally break everything they do. Make them do less...especially important things.
As a side effect...the statement: the government broke X so let's have the government ALSO do Y. (To fix it) is perhaps the most profoundly anti-libertarian statement frequently made by libertarian-leaning folks. Most commonly heard about immigration.