as is the nature of being an anarchist in the freedom movement, i have many minarchist friends. for those who don't know what these terms mean, an anarchist (an=no, archos=rulers) is one who advocates the abolition of government and a minarchist (min=small, archos=rulers) is one who advocates a government, but a small and weak government. though i certainly appreciate minarchists more than outright statists, there are some problems that i think minarchists should consider that make the minarchist position untenable.
as with all issues, there are two aspects: the moral and the practical. the moral is always the easiest to deal with, so i'll start with that. inherent in any "archism" that isn't anarchism, is the rule of some over others - by force. so, by definition, minarchists advocate an institution in which some people use violence to rule over the innocent as well as the criminal. they advocate the initiation of force to keep others out of certain markets like defense, justice, and police. some may even advocate more than that, but if so, that begins to strain even the minarchist label.
it should be fairly obvious that no one, including a minarchist, has the right to participate in any markets, while excluding others by force, nor does anyone, including a minarchist, have the right to force others to participate in a market that they have monopolized with their minimal state via such nefarious schemes as taxation (the forced taking of the property of others, aka; theft). even if elected, how can an electorate, each member of which has no right to rule over others, confer to the minarchist such a right? they can't. no one has any such right. such a right does not exist. therefore, the actions of the minimal state must be undertaken illegitimately.
generally, minarchists use the argument that a government is necessary for an orderly society and that certain markets must be monopolized by the state to achieve that. this is a practical argument, not a moral one. the morality of rule over others is still as clear regardless of practicality. the problem is that minarchists are, in this way, no different than totalitarians. they advocate the violent rule over others in order to achieve some goal. the difference is in degree, not in kind. totalitarians have the same philosophy, only with a wider scope.
now for the practical problems with minarchism. in advocating a state monopoly in certain markets, like "national" defense, justice or police, minarchists, wittingly or unwittingly, advocate socialism. socialism is an economic "system" in which government holds titled control over the means of production. in other words, the government holds a legal monopoly over a certain market or markets. it has been shown, both in theory and in practice, that socialism can't work for the good of society. the reason is that a coercive monopoly (a monopoly that insulates itself from competition by force) has no market input by which to determine demand for its goods or services, the correct resources and amount of resources to use for the goods or services, or the type of production to employ for those goods and services. there is no access to the pricing that markets provide (through competition) in order to calculate these things. a socialist system is, by its nature, excluded from the information necessary to make prudent decisions. This is widely known as "the calculation problem".
to minarchists: i know that the migration away from statism is a tough one and it takes time. you are on the right track! of course, it is my desire to help to bring you full circle and gently point out the reasons why government, of any size, is morally and practically wrong. luckily, i've also written briefly on how markets are more likely to succeed where governments inevitably fail, here, here, here and here.
take the leap to anarchism, minarchists (and everyone else)! we are here waiting to soften your landing.