If Murray Rothbard himself was sitting in front of me saying that anarcho-capitalists are not real anarchists, I would have to explain what capitalism is. I would help him to understand exactly why he’s wrong.
Capitalism: an economic and political system in which a country’s trade and industry are controlled by private owners for profit, rather than by the state. ~ Oxford Dictionary
The state, even if structured bottom up, is a collectively owned system where market failure reigns supreme due to everything it does being a public good.
Hear this: The only reason the state continues to function at all is due to coercive correction of its inevitable market failures. It literally uses violence to steal resources from its “citizens” (that would be you, part of the collective) in order to control them so they can keep stealing the money. Anyone who supports this sort of system is culpable to this theft. You directly contribute to the theft by voting in people that think up more dreamy ways to pick pocket you.
Then you have to have the tax collectors, and “law enforcement” which should be redefined as “thugs” since their primary objective is to enforce the edicts of their masters (this is you, statists). These enforcers have the lovely job of dreaming up new ways to physically assault you if you resist your pick pocketer.
Then the state gets to dream up terrible ways to corner markets while paying for more law enforcement and helping to “smuggle” products in… officials are elected to oversee everything and further the progression of larger and larger government. This is how you end up with the drug war, because it creates an intentional black market industry so the enforcers have someone to attack.
If one considers that which was stated above, and how toxic the state is. Then, one should understand that capitalism is completely at odds with the state. Capitalism is at odds with the state.
The corporation only exists because of governments. Governments ask you to register your corporation, so they can steal some money. In return, some corporations are given protection services for maintaining their monopoly. These special corporations are not capitalistic, because they involve using the state to modify the market in their favor. This is corporatism by force.
Anarcho-capitalists do not support this setup at all. They support anything you can do voluntarily with another person.
Anarcho-capitalism is the rejection of initiated violence. It is the notion that through voluntary actions beneficial to both sides of a trade, and the non use of justified violence, everyone is truly free.
To suppose that anarcho-capitalism is not anarchism is foolish.