Kev-o is unintentionally hitting a good point about the term Anarchy.
Ok... on the Word Anarchy.
The first Anarchist that i know of was William Godwin.
Godwin noted that most of societies catastrophes (Wars, plagues, etc.) were caused by struggles for property or land. (Wealth, property and land were all synonymous in the days when society was mainly agricultural) Godwin concluded that society would be benefited if 'private property' were abolished, which essentially meant, land/property that was held in the hands of an individual/small group rather than the whole of society.
Godwin then noted that, at the time, a significantly large portion of 'private property' was held in the hands of the State or those who were connected to the state. (Ex, king and clergy) Godwin THEN concluded that in order to abolish private property, it was necessary to abolish the state.
Godwin lived before the industrial revolution and had little conception of private property as it pertained to individuals who were separate of the state, or of justly acquired property through means of exchange. I think this is why so many anarchists insist that the idea of voluntarilly existent private property is utterly inconceivable.
Anarchists who followed Godwin usually treat Anarchism as an attempt to abolish private property or hierarchy, or both. And that the abolition of the State is ancillary. "Left Libertarians" will vary in the degree that they view the abolition of 'private property' and 'oligarchical heirarchy' as being paramount.
Some Anarchists hate the free market so much because of it's implicit assumption of private property and voluntary exchange that they will adopt pro-state positions simply to attack the free market. This is particularly profound with the followers of Chompsky. One Anarcho-Syndicalist hated the free market so much that he was willing to defend the military industrial complex just to 'prove' that the free market wouldn't be capable of advancing civilization's computer technology.
When an anarchist of this kind finally realizes that the abolition of private property cannot occur in a stateless society; they become a communist. The use traditionally conservative means [The state] To achieve leftist ends. This kind of approach is bizarre, reactionary, and utterly disastrous whenever applied.
"Anarcho-Capitalism" as originating with Molinari and developed by Hoppe and Rothbard, is, in a sense, not Anarchism, in that it doesn't attempt to abolish private property. But if the abolition of private property is a necessary attribute of Anarchism, then one would also have to agree that Bakunin, Spooner, and Thoreau were also not Anarchists either.
This is why many Rothbard seldom used the word Anarchy to describe his beliefs. (He usually described the government as being Anarchic in nature).
Now, with respect to the idealism of 'Anarcho Capitalism', let me say a few things.
1) Rothbard Deals Explicitly with scenarios pertaining to private Tyrannies. Never does he assume that abolishing the state would result in a perfect society, or that it would change human nature in the slightest.
2) "Statism" is idealistic in it's own sense. It assumes "Oh if only the right people were in power government rule would be functional." Ignoring the fact that no system of governance can distill any civic virtues or virtuous people. And that the more powerful the government, the less likely "Greedy" People will find their way into government instead of business.
And people who think that Democracy is capable of bringing these leaders into government has no right to call anyone else idealistic. These people have their heads in the sand as far as i can tell; One need only look at the mainstream political class, and have a talk with the average voter to realize that people live in the absence of any effectual means to control the actions of their leaders.
Relying on the "Market" assumes that people will act selfishly and to their own ends. This is NOT idealistic, this is as realistic as it gets. And if it just so happens that many people AREN'T selfish, then that's just as good.
Relying on the "State" Assumes that the State is a Dues Ex Machina motivated by benevolence and managed by "The will of the People". This assumption is as idealistic as it gets. And notions of "The Will of the People" are revealed to be mystical and unfounded when shown face with reality.
WAs the iraq War the "Will of the people"? What about the patriot act? Guantanamo? Government Debt? Vietnam? Obama's new healthcare Bill? The Stimulus? The Bailout
Stop calling yourself a realist when you throw your hands into the air and cry "The STATE will do it!" Every single time a problem arises you can't conceive a solution for.