> left anarchists know the state grows out of the conflicting class interests of the working class and capitalist class
> Propertarians believe that if you got rid of the government, the free market will sort things out because it's the gov. interference in private enterprise that causes societies conflicts
I think you've just given a slightly better summary of the magical thinking of each, rather than fundamentally disagreed with me.
Right-anarchists believe that destroying the state will finally allow capitalism to thrive, while left-anarchists believe that destroying the state will destroy capitalism too.
Partially this disagreement is simply about the meaning of the word "capitalism", though, which both sides chuck around unexamined without bothering too much about the fact that they have completely different definitions of this word, and that neither definition really matches what the man in the street means when he uses it.