Anarcho-capitalist here, ask me anything.

There are two general approaches that lead me there: the utilitarian and the ethical.

The utilitarian approach: I see lots of government interventions that, while allegedly well-meant, end up causing more harm than good. See https://en.wikipedia.org/wiki/Price_controls and https://en.wikipedia.org/wiki/Tariff for a couple of examples of clearly economically counterproductive policies that governments nevertheless engage in again and again; lots more are less clear but just as bad. Some of these are due to special interests somehow convincing the government, or voters, that the policy is net beneficial or virtuous or something, when it actually enriches the special interests at the expense of others. Some terrible policies are just due to naivete or lack of caring—and those who suffer from the policies not being a sufficiently well-organized political force to stop it. Others have more complicated explanations.

The common thread I see is, these are policies imposed by force on nonconsenting people. (The "social contract" theory is a rationalization that doesn't pass basic scrutiny. When a person opposes a policy and votes against it, and then 60% of the other inhabitants vote in favor of it, you can't meaningfully claim that the person has "consented" to the policy; that's not how contracts work. It's even less tenable when the votes are for politicians, who make decisions years later on issues that didn't exist at the time the votes were cast.) When those policies cause suffering to some people, it doesn't matter—they can't do anything about it, so the policy remains. Well, occasionally the suffering group is better at politics than whoever created the policy, but often they're not.

A question is, if these policies are so good, why do they have to be imposed by force? After all, if, for example, a policy would benefit three people by $100 worth and harm someone else for $50 worth, one could arrange for the three to each give, say, $30 to the fourth person, and then it would be +$70 for each of the three and +$40 for the fourth—i.e. it's net positive to everyone, and then it could be done voluntarily. (It might not happen in practice due to transaction costs, or if someone else holds out for a better deal, but one would expect something like it to happen eventually.) Every net-positive policy could be implemented voluntarily. The only policies that absolutely require force are those that are net-negative. Sounds like an excellent heuristic for policies to forbid. Only allow policies that are voluntarily agreed to by everyone involved.

Transaction costs are not zero (although technology tends to reduce them), and there are some things where a force-based approach looks simpler and more workable. And there are certainly hard problems—how to fund public goods and what to do when someone doesn't want to pay, how to have a stable society with multiple competing private police forces. Various people have proposed solutions; I suspect that at least some of them could be made to work tolerably well, and I think experimentation plus further technological development will make some of them clearly better than state-based alternatives.

I wouldn't advocate tearing down every government in the world today to switch to anarcho-capitalism. I do think it's a goal they should all approach, and that many of the paths in that direction (i.e. reducing government interventions) are obviously net-positive. (There do exist some policy kludges to make other policies less harmful, and if you canceled the kludges but kept the original harmful policies, you could be net-negative; you do have to be somewhat intelligent about it.) Some problems might not have anarcho-capitalist solutions that could be implemented today; some might never have them, I can't rule out the possibility. But I suspect it can be done; and anyway, if we only manage to cancel 95% of harmful government interventions and conclude we can't remove the last 5%, that'll still be a great achievement.

The ethical approach is this: The non-aggression principle. Physical force is immoral unless it is used to defend against or punish the aggressive use of force. You do need a concept of property and a notion of what counts as "force", but that's basically it; I think an ethical system has to be a Schelling point, which everyone might agree to without needing to communicate let alone negotiate, and I haven't encountered anything else nearly as good as this one. Anyway, it follows that all government interventions either involve aggressive force, and are thus immoral, or else they could be implemented by private parties.

Now, ethics aren't necessarily to be obeyed absolutely. Pretty much any ethical system will tell you that murder is wrong. But you can imagine scenarios where, say, someone with godlike foresight perceiving what Hitler was going to turn into when Hitler was still a child, and deciding to kill him first. (Somewhat more realistic are trolley problems and organ donor problems. Also genuinely realistic is a whistleblower engaging in stealing, lying, and possibly worse behaviors to exfiltrate the data. If the data is important enough, how far do you go?) My take is, the law must forbid such things—the law must be ethical—but individuals might rationally decide to step outside the law in extreme circumstances. When they do, they should bear in mind that (a) they now have no right to complain when good people use force to stop or punish them, and (b) ethical violations generally have bad second-order effects ("So, does that mean the guy with five healthy organs should expect the doctor to try to murder him, and therefore he should incapacitate the doctor first and skip town?"); but it's not impossible to conclude that breaking the law is still the best approach.

So, it's possible that a grossly unethical legal system—one which routinely violates the non-aggression principle—is the best choice in a tough situation. (Earth is a tough situation.) But there'd better be a damn good reason for each violation—which I expect there usually isn't. The violations should be scrutinized, and unjustified ones should be eliminated, as quickly as possible. We probably won't eliminate everything—any more than we can bring the murder rate to zero (and the most salient proposed societies with zero crime are dystopias)—but, again, every step in that direction is a good one, so let's go as far as possible.