The word "anarchy" is from the Greek, prefix an (or a), meaning "not," "the want of," "the absence of," or "the lack of", plus archos, meaning "a ruler," "director", "chief," "person in charge," or "authority." Or, as Peter Kropotkin put it, Anarchy comes from the Greek words meaning "contrary to authority." [Anarchism, p. 284]
While the Greek words anarchos and anarchia are often taken to mean "having no government" or "being without a government," as can be seen, the strict, original meaning of anarchism was not simply "no government." "An-archy" means "without a ruler," or more generally, "without authority," and it is in this sense that anarchists have continually used the word. For example, we find Kropotkin arguing that anarchism "attacks not only capital, but also the main sources of the power of capitalism: law, authority, and the State." [Op. Cit., p. 150] For anarchists, anarchy means "not necessarily absence of order, as is generally supposed, but an absence of rule." [Benjamin Tucker, Instead of a Book, p. 13] Hence David Weick's excellent summary:
"Anarchism can be understood as the generic social and political idea that expresses negation of all power, sovereignty, domination, and hierarchical division, and a will to their dissolution. . . Anarchism is therefore more than anti-statism . . . [even if] government (the state) . . . is, appropriately, the central focus of anarchist critique." [Reinventing Anarchy, p. 139]
For this reason, rather than being purely anti-government or anti-state, anarchism is primarily a movement against hierarchy. Why? Because hierarchy is the organisational structure that embodies authority. Since the state is the "highest" form of hierarchy, anarchists are, by definition, anti-state; but this is not a sufficient definition of anarchism. This means that real anarchists are opposed to all forms of hierarchical organisation, not only the state.