I plan to do a longer post some time in the future refuting minarchism, but for now you should read Gordon on the subject.
One part particularly stands out:
Why should one believe such a thing? Suppose people for the most part accept a libertarian scheme of rights — this, by the way, was the only circumstance in which Murray Rothbard considered viable an anarchist polity — would they not have, contrary to Lee, contract law without a state? (The issue, once more, is for now not whether this is likely but whether it is possible.)
This is exactly what the minarchists don't understand. Market anarchists aren't interested in what's "likely" or practical. We're interested in what could work, given the right circumstances.
So long as market anarchism is theoretically possible, the state is not justified.