I was having an argument one time with an "anarchist" that accepts capitalism(an anarcho-capitalist). I argued that anarchism is an ideology that advocates certain ideas(like abolishing private property, capitalism, and being against hierarchy). This person argued that anarchism is just the belief in the abolition of the state and nothing more. They said that anarchism isn't anti-hierarchy either, just abolishing established authority. So, rulers and government could still exist. As long as there is nothing "established".
Who is right?
or are we both mistaken?