: "Anarcho-capitalism" is self-refuting, a logical impossibility. It's a contradiction like "square circle" so it can't be discovered in any world.
Nonsense. "Anarchy" means without rule; Anarcho-capitalism calls for the abolition of rule. The only (not merely the best, but the ONLY) practical meaning of the word "rule" applies to a government. The extent to which anarcho-capitalism allows "rule" to exist (or "coercion", a term you would probably prefer,) is the exact same extent to which nature allows "rule" to exist.
Anarchists on the left like to think that "rule" means all hierarchy, which apparently includes rules of property ownership. Unfortunately, property is one of those things which is genuinely impossible to do away with. It rules us in the same sense that hunger or the weather rule us. (There is a hierarchy in our bodies which sometimes puts the needs of the stomach over the needs of, say, your foot. There is a hierarchy in the weather wherein the needs of the thunderstorm pay no heed to your desire not to get wet.)
"Property" is merely a way of saying "allocation of scarce resources." Since all the resources on earth are scarce, they must be allocated. We will never be free from this fact of life.
: "Anarchy" in the best sense of the word (freedom from coercion and other definitions along those lines)
Your definition of coercion is meaningless. Neither you nor I will ever be free from the "coercion" of property, hunger, or the weather.
McSpotlight: To be precise on this, 'anarchism' is derived from 'an-arkos' (Anc. Gr.) - meaning 'no leader'; it means the absence of any imposed power heirarchy.