The libertarian line is not actually a simple line of reasoning, but rather several interwoven ones. Because of assorted in-person fights on the topic...I figured I ought to attempt to set down the whole libertarian line in a single spot, understanding that libertarianism is a political direction (less government tends to be preferable), not a single position (no government is best).
Furthermore...it's important to understand that epistemologically (Aretae's 2nd favorite word, after iterative) no one (+/- 3%) believes any one thing for any one reason. Rather, (rational) people believe things for a host of reasons, all of which together (in Bayesian multaplicative fashion) mean that the sum total weight of belief on one side of an issue is at least a little more than the sum total weight on the other side of an issue. Careful thinkers remember that the sum total of arguments on one side of a position do not mean that the sum total of arguments on the other side are bad...and so tend to have positions between 50 and 60% certainty. However...it's also true that once one has a position buttressed by a dozen or so different lines of argument, then even demolishing a single line of argument doesn't have much effect.
Argument path 1:
The state isn't special. AKA "Lose the we"
Fundamentally, if one person shoots another person because he doesn't like what they're smoking, it's immoral. We call that person a murderer.
If 10 people agree to hire a shoot someone if they smoke something they don't like, it's immoral. We call that group a mafia.
If 1000 people get together, hire someone to shoot someone who smokes something that at least 500 don't like, we call that group a state, and most people decide that's ethically ok. Bullshit.
Same moral rules for individuals and state actors.
Argument path 2:
The notion of consent and common-good action is largely fictional AKA "exit over voice"
A party system wherein two rich groups of people use tribal instincts and media consultants to give a choice between two effectively indistinguishable choices is not "choice". It's damn close to a conspiracy.
A system that consolidates economic power produces public choice behavior where those people who care about (and are motivated to know about) economic power pull the strings. Necessarily.
A system with lots to regulate cannot be understood, or legislated by the people making the laws. Roughly all law-making will eventually be outsourced to un-elected, un-representative, un-accountable folks. Like our system.
A system wherein 70 % of the citizenry are eligible to vote, 60% of the eligible voters vote on a good year, 30% of the eligible voters are partisans of one side or another, and 50% of those partisans are partisans only because the other side sucks even worse means that any election is won by 6% of the population getting a candidate they would like. We call that a popular mandate...and allow the winner to make decisions that impact everyone.
Argument path 3:
Hayek, hayek, hayek.
Central planning is impossible to be efficient. Any decision made by central planners is certain to give people less of what they want in the short term than what they would choose via markets. The planner cannot have enough knowledge to make decisions, as most knowledge that makes decisions isn't even explicit knowledge. It's implicit knowledge, not yet formalized into a system by the knowledge's owner.
Argument path 4:
Iterativity & Error
Probably the best discovery in the past 50 years of business is that your first guess is always wrong...and you will find out after you try it. Your second guess is wrong too...which you will find out after you try that. The only path to getting good value for customers is to guess, and then update lots and fast. By observation, governments are hideously bad at updating. Laws and agencies especially are really bad paths towards solving problems, because they're especially hard to update (read get rid of).
Argument path 5:
Competition sucks very badly for the entities engaged in competition, and the customers of said entities benefit massively. Government intervention in the market 99% of the time reduces competition, rather than enhancing it. Any competition-reducing mechanism is primarily a method of transferring money from poorer folks to richer.
The key element in competition is allowing failed enterprises to die, and successful enterprises to live. Government works incredibly hard to prevent this. See: public schools, post office, etc.
Also, the government is monopolistic. Since it is monopolistic, it has no external standards to compare itself to, and will not improve at the speed that competitive enterprises do.
Argument path 6:
In the case where Al disagrees with Bob over what to do...in most cases, it's not because Al or Bob is immoral or obviously wrong...it's because they really, honestly, and at least semi-intelligently disagree. In this case, the solution of Al trying to get the gun that makes Bob do what Al wants seems full-on evil. In cases of real disagreement...9 times out of 10, the correct path is for Al to try Al's thing, and Bob to try Bob's thing...or Al to persuade Bob to try Al's thing. Offering to shoot Bob if Bob doesn't do it Al's way is almost always the worst option available...and the only option from the state.
Argument path 7:
States are evil.
In the history of the world...the greatest killer of people in history is germs. 2nd is states. Full stop. I don't even think there's room for argument on this as a historical fact. There is room to dispute whether all states are evil, or just most states are evil, or just states with some characteristics...but that most states both now and throughout history have been moderately actively evil is hard to deny. And, the more power they have historically had, the more likely to be evil (Lord Acton).
Also...See Hugo Chavez, Vladimir Putin, plus the usual mid-century suspects. "The Great" in history is short for "Killed a metric-ass-ton of people"
Argument path 8:
State actors *should* be evil.
Bruce Bueno de Mesquita has come as close as possible to a closed-form definitive game-theoretic proof of the optimal behavior for a state-actor. Universal correct response: Screw the citizenry, help your friends that keep you in power. Any other action is likely to result in your losing your job as state-actor. Far and away the best serious way to help your friend, without undermining his base of power that makes him valuable to be your friend is to limit competition with however he makes his money.
Public choice analysis plays here too. Any person acting as a state actor (shit...and person in any organization who wants to stay in the organization) must, in order to accomplish *any* goal whatsoever, accumulate both operative power, and staying power in order to accomplish said goal. Run this game theory for a few iterations, and it becomes true that for all realistic goals, the accumulation of power becomes the pre-empting goal #1. All state actors should have as their effective goal unlimited power.
Argument path 9:
States suck at whatever they do
By observation, for any given nominal goal, states are bad at it. If there is a non-state solution to *any* problem, it will be solved better by non-state action than by state action.
Freedom is an ultimate (political) goal. Freedom is not something you choose in order to get something else. Rather, freedom is a good in and of itself. There needs to be a presumption against violating freedom. Depending on how rabid you are (me: frothing at the mouth, about to die wolf), you can assert that this freedom is ultimate, or simply the default presumption. Every state action is an action against freedom. Bad.
Goal != effect
The question of government should not just be about goals, but rather about results. How well has the government war on drugs gone? Poverty? Terrorism? Iraq? By observation...the government methods used to attack problems have not solved those problems, but in many cases, made the problems worse. Perhaps, but not certainly, government is part of the problem, not part of the solution.
In particular, the problem of poverty is problematic. Poverty (by far) is the biggest problem in the world, both now, and throughout all of history. The key question around poverty is how to alleviate it. The government response to poverty in the Western world has been nothing short of atrocious. First, the government prevents the country from gettting richer, and second, it doesn't solve the problem. If we simply shot everyone involved with government provision of poverty programs in the USA, and distributed the money evenly to everyone in poverty in the states...I'm pretty sure that would work out to a moral win.
Folks like Will Wilkinson argue persuasively that the Scandanavian model: Get as rich as possible, and redistribute a lot to the poor is far preferable to anything anyone else is doing..
The Principal-Agent problem
Government is composed of individuals. Those individuals have goals. The citizens/electors have goals. The elected politicians have goals. At 2-levels removed, there is no reason whatsoever to expect that government actors should be acting in the electors' interests.
Government primarily maginfies the power of the already powerful
If the government does little, then the powerful have to rely on their own resources in order to get what they want. If the government does lots, then the rich and powerful can effectively lobby the government to additionally solve their problems rather than not interfering, and this result is far more likely than the poor successfully lobbying government actors to protect the poor from the rich.
The government displaces other solutions
Before the government offered welfare, private entities ran soup kitchens. Now the government runs all anti-poverty programs, and makes laws preventing non-government ones from serving unhealthy food.
Before the government offered public schooling, kids were almost universally literate (in the USA). Now private schools are a tiny fraction.
Before the government stepped in, offering welfare, AFDC, husband substitutes...the black marriage rate was pretty high. Now it's pitifully low.
When the government acts, it displaces the other, sometimes community, sometimes private efforts to solve the problem. Often the solution provided by the government is less effective than the private solution was. Certainly, the government solution evolves less well.
Organizations exist to serve themselves
For all organizations, the size of the organization, the age of the organization, the likelihood/possibility of the organization going out of business (losing customers), and the quality of the feedback mechanism from the customers are the primary factors that determine how good the organization is at serving its customers. The US federal government is the 250 years old biggest organization in the world, and has no fear at all of going out of business, and gets crappy yes/no feedback roughly every 4 years. It should be the worst-run organization on the planet for the purpose of serving it's customers. It's close...because most of the worse ones aren't there to serve the customers.
Complex systems, unintended consequences
The modern social/economic system is tremendously complex. Any action in a complex, non-modularized system has both intended and unintended consequences. See, for instance medicines. Medicines to help with erectile dysfunction help to cause heart-attacks. See for instance, biosystems...the introduction of ferretts to chase down rabbits has been known to cause ecosystem collapse. See for instance the economy. Government intervention screws up complex systems badly.
Also, re-referencing the decline of the black family, which was predicted by my black grandmother-in-law when welfare was introduced. She thought Welfare was a deliberate plot to destroy the black family. I personally don't figure government is that smart.
Prohibition and the drug war have created more crime than any other government actions we can find. While that's known now, and why police and prison guard unions massively support the drug war now...I don't think that the goal of either was to massively increase crime?
Government != society
Oftentimes arguments against libertarianism, there is a conflation of Government and Society. Government is not society and society is not government. Government is a small group of people in society who have somehow managed to grasp the reins of violence, and the treasury. Society is usually a group of people who'd like to live their lives, and help their neighbors. Government are the people who prevent you from giving your used toys to needy kids because they might not be perfect toys. And then they take your money, and buy new toys and give those toys to the needy kids.
Trade is effectively always good
Trade is what happens when you have an orange that I'd be happy to buy for $2, you would sell it for $1, and then you sell it to me for $1.50. I'm 50 cents richer than I was before the transaction...and so are you. Trade is good...3/4 of the total value in the world comes from moving stuff from low-value states (posessed by someone who doesn't want it much) to high value states (posessed by someone who wants it more).
The government's entire interaction with trade is to prevent it...or make it flow to politically connected constituencies.
Regulation is almost always supported by big business, but hurts small business
As a near-universal truth...regulation is more easily navigated by large organizations with swarms of lawyers than by small firms with few lawyers. Further, fixed cost regulations (almost?) always fall harder on smaller firms than on larger firms. As a general rule, one can find the big players in any given industry as strong supporters of any given regulation...as it gives them a competitive advantage, and a barrier to entry. Usually, this (net) screws the consumers. From personal experience...Blue Cross was heavily involved in drafting ObamaCare...and it has far greater impact on smaller insurers, than on big ones.
Wealth (social, individual, whatever) is the single biggest measureable factor impacting the quality of life in the world. Wealth is almost entirely a function of invention, and trying new things. Invention is almost entirely a function of competition...new firms trying to out-compete old firms (existing companies don't innovate and break existing lines of business...it would be stupid to). Governments do a whole darn lot to protect incumbent firms, and generally heavily bias the playing field away from upstarts. In doing so, governments destroy huge amounts of wealth. This is full on bad.
Which countries have become richest in the last 60 years? Singapore, Hong Kong. How much government? Very little. Low government action, especially low regulation, but also low taxes highly positively correlated with high wealth. Compare wealth of Singapore vs. wealth of North Korea or Cuba 1960 vs. now. Which system is better? Heck...Singapore appears to be the best system on the planet for the poor people of the country.
We don't know the right answer. We're just not that (collectively) smart. Trying to legislate the right answer is crazy. We need, desperately, to keep looking for better answers....not to lock a single answer in place.
Overall, there are a lot of lines that point loosely in the libertarian direction. None of this means that libertarianism is correct...or that libertarianism is a better solution than progressivism or conservativism. However, it does mean that there are a lot of reasons to lean in (or move closer to) a libertarian direction, regardless of what your other predilections are. Unless, of course, you're in government, in which case, your prime directive to accumulate more power (so you can do what you need to, unimpeded) is most threatened by libertarian sentiment.
What did I miss? Is this categorized well?
UPDATE: I've added more in part 2, mostly based on great feedback.