There are a great many answers which have been offered. Some anarchists, such as the emotivist and (paradoxically) the moral anarchists have little interest in high-level moral theory. But this has been of great interest to the more intellectual sorts of anarchists.
One popular argument for anarchism is that it is the only way for true socialism to exist. State-socialism is unable to actually establish human equality; instead it simply creating a new ruling class. Bakunin prophetically predicted the results of socialists seizing control of the state when he wrote that the socialist elite would form a “new class” which would be “the most aristocratic, despotic, arrogant, and contemptuous of all regimes”. Elsewhere Bakunin wrote that “[F]reedom without Socialism is privilege and injustice, . . . Socialism without freedom is slavery and brutality”. Of course, socialism itself has been defended on both deontological and utilitarian grounds, and there is no need to repeat these here.
On the other hand, anarcho-capitalists have argued that only under anarchism can the Lockean rights to person and property so loudly championed by more moderate libertarians be fully respected. Any attempt to impose a monopolistic government necessarily prevents competing police and judicial services from providing a legitimate service; moreover, so long as government exists taxation will persist. The government’s claim to defend private property is thus quite ironic, for the state, in Rothbard’s words, is “an institution that presumes to ‘defend’ person and property by itself subsisting on the unilateral coercion against private property known as taxation”. Other anarcho-capitalists such as David Friedman find these arguments from natural Lockean rights unconvincing, and instead take up the task of trying to show that Adam Smith’s utilitarian case for free-market capitalism applies just as well to free markets in defence services, making the state useless as well as dangerous.
Still other anarchists, such as Lysander Spooner and Benjamin Tucker as well as Proudhon, have argued that anarchism would abolish the exploitation inherent in interest and rent simply by means of free competition. In their view, only labour income is legitimate, and an important piece of the case for anarchism is that without government-imposed monopolies, non-labour income would be driven to zero by market forces. It is unclear, however, if they regard this as merely a desirable side effect, or if they would reject anarchism if they learned that the predicted economic effect thereof would not actually occur. (Other individualist anarchists have argued that contrary to Spooner and Tucker, free banking would lead to a much lower rate of inflation than we experience today; that rent and interest are not due to “monopoly” but to scarcity of land and loanable funds; and that there is no moral distinction between labour and rental or interest income, all of which depend upon a mixture of scarcity, demand, luck, and effort.)
A basic moral intuition that probably anarchists of all varieties share is simply that no one has the right to rule another person. The interpretation of “rulership”, however, varies: Left anarchists tend to see the employer-employee relationship as one of rulership, and anarcho-capitalists are often dubious of the claim that envisaged anarchists communes would be democratic and hence voluntary. A closely related moral intuition, again widely shared by all sorts of anarchists, is that each person should exercise personal autonomy, or self-rule. One should question authority, and make up one’s mind for oneself rather than simply following the herd. Again, the interpretation of “personal autonomy” varies: The left-anarchist sees the employer-employee relationship as inherently violating personal autonomy, whereas the anarcho-capitalist is more likely to see personal autonomy disappearing in the commune or collective, regardless of how democratically they run themselves.