I am not a Libertarian, but I devote a lot of time to thinking about libertarianism and reading libertarians. Why? Well, the answer to that question depends a lot on the libertarians I am thinking or reading about. I divide libertarians into three sorts:
1. Marginal Libertarians: For most policies, these people think the next policy step should be in a libertarian direction, but they don't necessarily want a libertarian state. So of all the realistic policies we might adopt towards health care, the marginal libertarian wants the one that has less government intervention in the marketplace, less government subsidies, etc. Maybe he likes Paul Ryan's plan. But, unlike a traditional libertarian, he doesn't necessarily want government OUT of healthcare. At the margin he prefers libertarian policies, but going all the way to a minimalist state scares him.
Obviously more people are *mostly* marginal libertarians, than are *completely* marginal libertarians, since it is more a coincidental or attitudinal thing ("hey, look at that! Most of the policies I like involve less government!") than a real ideology. Greg Mankiw is an example of a marginal libertarian. Or Tyler Cowen.
2. Consequentialist Libertarians: Consequentialist libertarians think the marginal policy move should be in a more libertarian direction, but they also think that those policy moves should go all the way, and we should have a night-watchman state, or anarcho-syndicalism, or whatever. They want this because they think those kind of states are simply the best way to arrange public affairs, IE that adopting a minarchy has better consequences than adopting other forms of government. They aren't much interested in libertarianism as a philosphy, they see it as a practical and superior form of government.
I tend to think of Scott Sumner as a consequentialist Libertarian, though he may be more of a marginal libertarian. In general I think very few people fall into this category, and I don't spend much time thinking about it.
3. Philosophical Libertarians: Philosophical libertarians think a libertarian state would have good consequences, but they also think it is philosophically mandatory. They think government simply has no right to engage in redistribution, for example, and that this is as much a moral evil as theft. Or maybe they don't go that far, but on some level they think there is a *moral*, as well as a practical case to be made for minimal government.
I am just going to pick the obvious example and say Robert Nozick was this kind of libertarian. Or at least, was when he wrote Anarchy, State, and Utopia. But this category obviously includes people with muddier thinking. Ron Paul, say.
So why do I care about libertarianism? Because I am close to 1 and detest 3. In terms of category 1, I've been convinced on the merits that a lot of policy should move in a more libertarian direction. I am for free trade, open borders, less local regulation of property (IE, "zoning," height restrictions, etc), less incarceration etc. I still have big soft fuzzy liberal notions that keep me from identifying as a libertarian (hooray obamacare!), but I can read Tyler Cowen's blog and "right on" more than I "tsk tsk." So I tend to enjoy reading and thinking about consequentialist libertarians, even when they disagree with me.
In terms of category 3, I pay attention because a lot of philosophical libertarians are, to me, terrifyingly counter-majoritarian , rejecting the basic
Democratic Focused, Rights Focused, Rule of Law Focused Cultural Norms + Democracy + Rights as Side Constraints = Sound Government
formula that worked increasingly well over the 20th century. So, for example, here's a law profesor, Glenn Reynolds, who came on Russ Robert's show to talk about all the ways he would like to change the constitution in order to ensure that his policies always win. His proposals run the gamut of ways you can fail to respect modern democracy, from changing long established process rules to make the outcomes you want more likely (IE, fiddling with term limits, which he wants to do), to constitutionally forbidding democratic outcomes simply because you don't like them on policy grounds (IE, instituting a balanced budget amendment, which he does not oppose and only does not support because he thinks it won't be stringent enough), to undermining human rights when you find them inconvenient (IE, he wants a constitutionally mandatory poll tax, currently forbidden by the 24th amendment and probably by Article 25 of the ICCPR, an international human rights treaty we have ratified).
That's modern philosophical libertarianism: "We are clearly right as a philosophical and policy matter, but modern democratic government keeps not doing what we want. Therefor, democracy is flawed and the government is only failing to recognize our obvious rightness because it is in thrall to special interests. Therefor, we should limit democracy not just when it steps on human rights, but more generally whenever it fails to enact the policies we want. Convincing people to vote libertarian is all well and good, but most important is to take away or limit their ability to vote for non-libertarian outcomes." The US constitution's model, limited powers for federal government to guard against tyranny, but broad powers for state government to empower the people, has been turned into a radical new model: limited power for all government, not for the purpose of preserving democracy, but in order to make sure all our preferred policies win. It's a sickening rejection of majoritarian rule.
Add the distrust of democracy in with the utopianism, the blind conviction in an over-simplified philosophical position, the bad economics, the confident predictions of imminent doom for western democracies (doom that will conveniently reveal the status quo to have been flawed and libertarians right all along), the revolutionary rhetoric, and the on-campus appeal and you get a movement that reminds me uncomfortably of American communism in the 20th century. I'm not sure if movement libertarianism has the potential to actually be as dangerous or global as communism was, but I don't think it's worth finding out. Philosophical libertarians, from Ron Paul to law professors on Econtalk, have terrible ideas. Those ideas have to be engaged. Doubly so since so many of their policy positions coincide with my own, and since it worries me when my beliefs about, say, ending the drug war get lumped in with the beliefs of someone who wants a constitutionally mandated gold standard, or something.
So, that's why I spend a lot of time thinking about philosophical libertarianism.
Obviously, not all philosophical libertarians fit the description I just painted (most don't, probably. The most wrong voices are probably the ones I am most likely to remember), and I try to be charitable to the best arguments philosophical libertarianism can present (which are pretty good!). Just as obviously, plenty of people who hold a few views I find objectionable are probably smart people with lots of other good views (I am sure Reynolds, the law professor I talked about above, is smarter than me and has better ideas than me about most things, he just has really bad ideas about whether the constitution should be amended). I am trying to demonize ideas, not people.