Anarcho-capitalism is a social system that aims to maximize freedom. It does this by combining the peaceful coexistence of libertarianism with the optimal productivity of laissez-faire capitalism. Peace is important because any conflict between people reduces at least one person’s freedom. Productivity is important because every bit of capital that people produce increases someone’s freedom. So to have the best life possible, we want to minimize conflict and maximize capital.
Libertarianism minimizes conflict with one simple rule: do not cause conflict. All other libertarian ideas like “stealing is bad” are derived from this non-aggression principle. The non-aggression principle limits the freedom of individuals by forbidding certain behaviors like theft, murder, etc. Though this rule directly reduces everyone’s freedom, it tends to produce a society with more freedom than a society with no rules at all. You don’t get to kidnap other people but, likewise, other people don’t get to kidnap you. So while libertarianism is a constraint on you, it also frees you from conflict with other people. Conflict has the potential to greatly reduce your freedom, so avoiding it can be very valuable.
On the other hand, capital has the potential to greatly increase your freedom. Knowledge, wealth, and technology can make life more comfortable and more fun. Libertarianism maximizes capital production by creating the environment in which people are most productive. One reason is that in a libertarian society those who produce keep the full benefit of their efforts. Another reason is the powerful effects of cooperation. When people cooperate, they are able to produce more together than individually with the same amount of work. The more people that work together, the more productive and wealthy they become. Conflict prevents cooperation, so libertarianism allows for maximum cooperation.
Capitalism is a libertarian social system with no other rules. It turns out that so long as liberty is protected, society advances most quickly when people are free to do as they please. Throughout history people have created systems that diverge from this by adding additional rules, or shying away from the NAP, but none have worked better from the perspective of freedom. For example, an Amish society has rules that inhibit the development of advanced technology. English Puritans had rules for communal ownership of property. There have also been, and still are, many societies that do not uphold the non-aggression principle. In general, anything like this will lead to less capital production than a capitalist system.
Straying from the NAP or adding any additional rule limits everyone’s freedom and, in general, the less freedom people have the less productive they are. If you remove the NAP, freedom in the real world is reduced greatly with the only benefits accruing to thieves, murderers, and the like. On the other hand, if you add additional constraints on freedom, you reduce everyone’s freedom, with some short term benefits for some people, and long term freedom reductions for everyone.
The extent to which a system upholds the non-aggression principle and does not have additional rules is the extent to which it is capitalist. Since anarcho-capitalism is fundamentally about maximizing freedom, the system it advocates is this pure, libertarian capitalism. Despite the name, anarcho-capitalism does not explicitly prescribe capitalism. It merely supports whatever social system produces the most freedom. It just so happens that for large societies, capitalism is that system.
If magic were real and could free people to fulfill their desires more quickly and efficiently than capitalism, then anarcho-capitalism would embrace magic. The same goes for socialism, communism, etc. Ancaps would be all for them if they worked better in practice because anarcho-capitalism values freedom without specifying how to achieve it. However, as societies have discovered time and again throughout human history, there are no short-cuts to prosperity. People are most productive when those who pay the costs of production reap the benefits. Systems like communism which disconnect income from work incentivize people to work less than they otherwise would. When people work less, there is less wealth to go around, and in some cases this leads the entire society into poverty.
So ancaps recognize that the fastest way to greater freedom is slow and steady capital accumulation. They want to maximize freedom, but not at the expense of other people. We are the ones who love wealth and technology for giving us more freedom, and recognize that freedom is the first step in producing wealth and technology.
Anarcho-capitalism is not a system for organizing a family or a business. It is a system general enough to apply to all of humanity. It has simple rules with complex consequences and it is our best hope for the future of freedom.