Conveniently, the following excerpts from Libertarian Democraphobia relieve me of the effort of having to describe in my own words what I think are some of the fundamental problems of Libertarianism:
The libertarian non-coercion principle is a good abstract first approximation of the liberal presupposition that persons are free and equal. No one has a natural right to rule over another, and no one has a natural duty to obey. The liberal presupposition sets a high bar for the justification of coercion, and thus the justification of the state. Many libertarians think there is no justification. Therefore the only acceptable rule of collective choice is unanimity or full consensus. This is one focus of the debate between anarchist and limited-statist libertarians. On the anarchist side, political power cannot get off the ground, and thus the design of mechanisms to control political power is a non-issue. On the limited-statist side, political power does get off the ground, and thus so does the design of constitutions and democratic institutions. [...]Cafe Hayek (especially blogger Don Boudreaux) is, in my opinion, completely mired in "impotent, self-righteous grousing".
In any case, libertarians often display a confusing or confused reaction to democracy as it actually exists. The scheme laid out in most libertarian ideal theory is so distant from actual democratic practice that the whole existing system can seem by comparison a comprehensive injustice. When one’s ideal theory implies that politics is by its nature illegitimate and corrupt, one tends to develop a sharply disapproving attitude toward participation in politics. Lots of libertarians, for example, think it’s morally wrong to vote. (There are many structural reasons the Libertarian Party is hopeless, but here’s one reason libertarians tend to be at best half-hearted political activists.) Likewise, incrementalist approaches to policy can never be adequately pure from the perspective of radical libertarian ideal theory. School vouchers are still tax-financed; a system of mandatory personal retirement accounts has a restriction on economic liberty at its heart; and so on. So, not only is politics corrupt and corrupting. There are few democratically feasible libertarian policies that merit support. The public does not want libertarianism. Which means that the public does not want a system that respects fundamental rights. So much the worse for the public, the thinking tends to go. [...]
If libertarians are going to shift the politics of the countries we live in, we’ve got to get it through our thick skulls that many people have considered libertarian ideas and have rejected them for all sorts of decent reasons. We’ve got to take those reasons, and those people, fully seriously and adequately address them. Otherwise, we should probably just accept that libertarianism is a niche creed for weird people and reconcile ourselves to impotent, self-righteous grousing.
The irony is that The Fatal Conceit by Hayek is proudly displayed on their website, and the fundamental concept of The Fatal Conceit is that sweeping away all of society's institutions in order to remake society according to better principles is a really, really bad idea, yet this is exactly what the Cafe Hayek bloggers would do in an instant if given the chance.