You seem to be confusing anarchism with libertarianism. Libertarianism is basically capitalism on steroids; it's an individualistic, "rules-are-for-little-people" ideology. Anarchism is any of several different kinds of non-hierarchical socialism.
For clarity, by "socialism" I don't mean Robin Hood socialism, taking from the rich to give to the poor; that's coercive. I mean that socialists aim for a more-equal society. So I'm saying that anarchists are people that aim for a more equal society, and hope to achieve that using processes and structures that minimise hierarchy.