The biggest problem with libertarianism (and liberal social policies in general) is that libertarianism relies on people to recognize their own personal responsibility in their actions.
For instance, if I choose not to go to work today, that was a choice that I made and I need to deal with the consequences of maybe not having enough food to eat. Or, if I decide to go to the beach nude, I may have to deal with ridicule and people asking me not to be naked in front of their children.
In these days, people would rather bitch to someone else and make them responsible.
We can't have liberal attitudes toward ourselves and our actions until people stop relying on other people to enforce equality and responsibility.
No, the biggest problem with libertarianism is that it relies on people to recognize
what he judges to be "their own personal responsibility". (Which is why it's, "Good luck with that," AKA "LOLbertarianism.")
The libertarian fails to acknowledge that his ideas belong solely to him. He declares them "objective ("rational")", uses that to mentally foist them off onto everyone else, then declares everyone who does not align with his beliefs to be ideologically "incorrect" while distancing himself from any requirement to promulgate said beliefs. "If only everyone thought what I think they should, when I think they should, and acted how I think they should, everything would work great!" But his perspective isn't radically less self-centered than the conservative who sees nothing incongruous between, "Deez filthy blacks shouldn't be allowed to even look at our wimminz," and, "I'm 'murrican! I has rights!" He doesn't see all possible viewpoints so it's guaranteed that his ideologically "perfect" world isn't balanced, leaving inhabitants remaining with some very valid gripes over its nature.
Conservatards may not be very bright, but even they can figure out that you're not going to have resolution between conflicting viewpoints without sufficient power to force a resolution. Our decisions are going to be imperfect, unfairness will exist, but we can do no better than our best, and each has to move forward based on their judgment. The government that is the summation of individual judgment as to its best practices and possesses the fraction of power assigned sits over individual personal conflicts.
Libertarianism is really just teenage, whiny rebelliousness. "Why can't I do whatever I want with nobody telling me nothin'? I wasn't plannin' on hurtin' anybody, I just wanna do whatever I feel like."
You can only successfully chart a course that can't come into conflict with a person if you
are them. You aren't. So that doesn't work. This is why people have implemented a system that gives them some say over what others do. Spoiled white teenage males crying that it's unfair that their privilege wasn't extended into being the sole arbiters of what behavior of their is allowed doesn't really form a compelling argument that there's a burning need to implement this. Quite the contrary, as the degree of self-absorption they exhibit says that they're nowhere near ready to judge such a thing.