An anarcho-capitalist believes that man is his own master. He sees himself as the owner of his time, talents, and labor. Thus he argues that every individual has the absolute right to rule over anything he can acquire through the productive application of his endowments---as long as he does not violate the rights of others to acquire property in the same way. He understands fallen human nature and the need for a mechanism to protect human life, liberty, and property. Why would he want to abolish the state then? He is an anarchist because he sees abundant historical proof that the state is not only incompetent to provide adequate protection of our freedoms but is also predisposed to act as an oppressor, a chief violator of individual rights. In the absence of nation-states, there will be no national armies to start wars while the free market is assumed capable of providing law and order by expanding the role of already functioning private protection agencies and courts.
An anarcho-communist argues that man with his endowments belongs to his community: village, tribe, nation, or human race. He believes in the natural goodness of man and fights to abolish the state as a source of social injustice: producing inequalities; supporting hierarchies; stirring the unnatural evil passions of selfishness, greed, and envy; inciting political and economic competition and conflict. Unlike most revolutionary socialists, he understands that tyranny can only beget tyranny and rejects the possibility of a dialectical transformation of a "dictatorship of the proletariat" into total freedom. With the abolition of private property and wage labor and the elimination of the coercive powers of the state, all social contradictions will be solved and a new age of peace, love, and cooperation will commence. Instead of depending on market prices to convey information, in an impersonal way, about which activities are socially beneficial, the new man, free from his economic and political chains, will serve his fellow man face-to-face.
There are, of course, different flavors of these two main branches of anarchism, but a Christian cannot find safe haven in any such camp. In our opposition to totalitarianism we must be aware of the dangers of turning freedom into an idol. Soon after the fall of the Berlin Wall, Pope John Paul II warned us in his Encyclical Centesimus Annus that detaching freedom "from obedience to the truth" will turn it into "self-love carried to the point of contempt for God and neighbor." As tempting as any Utopia might sound, a Christian should be able to recognize the source of such lies and see "the contradiction in his heart between the desire for the fullness of what is good and his own inability to attain it and, above all, the need for salvation which results from this situation."
P.S. Here's a thought-provoking "libertarian" sermon on Passover.