Anarchism has in common with Liberalism the idea that the happiness and prosperity of the individual must be the standard of all social matters. And, in common with the great representatives of Liberal thought, it has also the idea of limiting the functions of government to a minimum. Its supporters have followed this thought to its ultimate logical consequences, and wish to eliminate every institution of political power from the life of society. When Jefferson clothes the basic concept of Liberalism in the words: "that government is best which governs least," then Anarchists say with Thoreau: "That government is best which governs not at all."
In common with the founders of socialism, Anarchists demand the abolition of all economic monopolies and the common ownership of the soil and all other means of production, the use of which must be available for all without distinction; for personal and social freedom is conceivable only on the basis of equal economic advantages for everybody. Within the socialist movement itself the Anarchists represent the viewpoint that the war against capitalism must be at the same time a war against all institutions of political power, for in history economic exploitation has always gone hand in hand with political and social oppression. The exploitation of man by man and the dominion of man over man are inseparable, and each is the condition of the other.
"Liberalism" in this case refers to classical liberalism, which is the 18th century political philosophy out of which both of today's "liberal" and "conservative" camps were sprung. We still find in conservatism this preoccupation with limited government; and, in liberalism, a certain conception of rights guaranteed or respected by the state.
Classical liberalism was important at the time because it was the first western attempt to locate rights at the level of the individual. For a long time, kings ruled under a presumed legitimacy granted to them by God. Then, around the same time, you had the development of both classical liberal and democratic ideas. As we have said, Liberalism pushed this idea of individual rights, a private sphere that could not be transgressed by the government. Democracy on the other hand, at least in Rousseau's formulation, served as a powerful indictment of monarchy; but his "general will" proved extremely dangerous as an absolute formula with no space for Liberalism's "private sphere."
Socialism developed in response to the centralizing tendencies of industrial capitalism, which relocated Liberalism's privacy for individuals into an abstract legal construct known as the corporation. Socialism intended to put whatever was productive under the democratic control of communities; but it fell into many of the same traps of the earlier democratic era: it eliminated all private life in its attempt to cull only one. Put differently, whatever began as genuinely socialist was quickly subsumed by the state.
This brings us to Rocker's passage above. Among the many different strands of contemporary western thought, Anarchism remains truest to the classical liberal ideal; it might best be described, to paraphrase Chomsky, as classical liberalism adapted to the modern era. The important point is that it is comprised of a combination of things; and you can find in it even a relationship to modern conservative thought -- a useful thing when we want to propagate our values amongst the Tea Party-types.