Efficiency: Here's another way to get to anarchy. Efficiency. We live in a world of physical things (including ourselves). Control of these things can be looked at a lot of ways, but the simplest is a binary division. All things are either private property, or public property. It is a striking fact about the world that where there are similar goods or services provided publicly and privately, the privately provided ones are better.
Our public schools, for instance, range from very good to abysmal daycare prisons. Spending is tremendous. Private schools, by contrast, don't have any bad examples (or very few), and they are cheaper to boot.
Another example? The provision of protection. In the inner cities, protection is mostly public, being provided by the police. People are generally forbidden to effectively defend themselves. In suburbia, there are many things guarded by private guards, who do a much better job of protecting them. In our more rural states, people are allowed to bear arms to protect themselves, another private means of protection that works.
How about another? Adjudication. The government court system is woefully overwhelmed with cases. Minor cases get almost zero attention; major ones can spend years in the system. A trial by a jury who know nothing special is a bad way to settle many specialized disputes. In contrast, arbitration offers speed and informed judges.
How about news and reporting? The State gives us NPR. The private market gives us a thousand sources, many of which are pro freedom.
Mail? The State gives us the USPS. The private market, FedEx, UPS, Airborne Express, etc.
Retirement? The State: ponzi scheme. Private market: stocks and bonds.
In fact, looking at the many things the government does it is hard to avoid the notion that the State has a sort of reverse Midas touch. Whatever it does turns to shit. There are good reasons for this, to be found in economics: competition; the problem of agency and control; etc. But we don't necessarily need the reasons to notice the problems with government services. Now, generally efficiency is a good thing. Efficient provision of goods and services means we are not wasting money, meaning we are richer. We have more money to spend on other things. Efficiency is a good thing, and the government is inefficient. It is reasonable, then to start wondering: how much of this stuff can we privatize?
A libertarian would say, we should privatize everything but the core functions of government: judicial, legislative, and executive. These things, of course, must be public.
Anarchists say, of course? Nope - let's privatize all of it.