Anarcho-capitalist critique of left-anarchism
Anarcho-capitalists like many things that some utopian anarchists like William Godwin or left-anarchists like Michael Bakunin wrote about individualism. However, They don't quite follow Bakunin in his complete acceptance of Marx's "das Capital". Actually, anarcho-capitalists don't accept the distinction between a "personal" sphere of activity and an "economic" sphere of activity - they only see one sphere, the sphere of Human Action.
Anarcho-capitalists consider that libertarian socialist notions about power, hierarchy, command and obey, etc., are rather childish - they think it is legitimate for individuals to voluntarily enter relationships where one obey the other on some purposes, presumably in exchange of some other service. What they oppose is the means by which some might obtain obedience, by force or fraud - but this is just like they oppose robbery and racket in general, and has nothing to do with obedience to some orders in particular.
Anarcho-capitalists consider as ridiculous the want of liberty without ever acknowledging the dual notion of responsibility.
Anarcho-capitalists defend the right of individuals to freely organize in cooperatives; but they resent the claim of most libertarian socialists that people should be forced into such cooperatives and that even willing, they should be prevented for their own sake to enter or defend employment contracts. They also think that cooperatives are usually a bad idea, because people are risk-averse, and it is irrational for them to have all one's stock in one company (one's cooperative); they think that workers would rationally seek to spread their risk by diversifying their stock portfolio. See this article about Entreprise in a Free Society.
Like individualist anarchists, anarcho-capitalists think that individuals exist before any collectivity and that no collectivist decision (and they reject a dichotomy between economic and personal matters), may hold without the prior consent of individuals. Anarcho-capitalists thus loathe the 'democratic' kind of collectivist control meant to happen in socialist anarchism, and wonder on which grounds socialist anarchists decide at which scale democracy should be held instead of whichever other scale - and whose opinion is to prevail when there is disagreement.
Anarcho-capitalists think that libertarian socialists either avoid or miss some essential issues concerning justice and protection: judicial prosecution, law-making and law-enforcement - how it is possible to avoid and resolve conflicts in a free society without resorting to any kind of government. They consider that property rights are exactly the conceptual tool required for a justice system to exist without the need for centralized law-making and law-enforcement.
Finally, anarcho-capitalists dispute left-anarchists' claims of being the one, true, oldest and original anarchist tradition. They claim that their own anti-statist tradition at least as old, and much more coherent with their individualist theories than with any collectivist theory.