Neither Anarchy nor Minarchy is Necessarily Libertarian
His more fundamental mistake is in seeing this as an argument on the minarchist side of the debate. Once you set up your limited government, you too have no way to guarantee that what it produces will be libertarian law. If law is made by direct democracy, the majority might vote to ban heroin or prostitution. If it is made by representative democracy, the representatives might so vote--especially if the position is supported by most voters. If the law is to be kept free by the courts, the courts might come down on the wrong side.
The only complete solution to this problem is to cheat--to define your preferred system in terms of outcomes as well as institutions. Thus a libertarian anarchist might say that the society he advocates is an anarchist society that produces libertarian law, and similarly for a libertarian minarchist. In either case, once the institutions actually come into existence, they will not be constrained by how their advocates defined them.
There is, however, a partial solution, at least on the anarchist side of the argument--one I sketched in my Machinery of Freedom and, in somewhat more detail, in a later essay. The market for law in an anarcho-capitalist society will tend to produce economically efficient law for reasons related, but not identical, to the reasons that other markets tend to produce efficient outcomes. Libertarians believe that freedom works, that libertarian law is closely, if not perfectly, correlated with efficient law. If that belief is correct, there will be a strong tendency for the market for law to generate libertarian law.
So far as I know, no comparable argument exists for the minarchist side of the debate, no good reason, short of assuming that everyone has become a libertarian, to expect law produced by political mechanisms to be either efficient or libertarian.
Neither anarchy nor minarchy is necessarily libertarian. But anarchy comes closer.