I'm falling for the "someone on the Internet is wrong" trap, but neverthless: Anarchocapitalism is fundamentally flawed because it rests on the assumption that capitalist markets optimize for the best utility function. They don't. Further, even in the optimization they do provide, they are flawed. Capitalist markets are powerful optimization systems, but they routinely fail, in pretty well described scenarios. Namely:
1. Wherever there are externalities, capitalism fails. For negative externalities, individual entities are motivated to capture the positive value, burdening the whole with the negative. For positive externalities, individual entities are not motivated to absorb the negative value when they can't capture the positive one.
2. Capitalist markets are, on aggregate behaviour, short-term oriented. This is a risk reduction strategy, but society requires some long term investments. Some of these long term investments also classify as positive externalities.
3. Pure capitalist markets have no provision for wealth redistribution and tend to accumulate wealth. While this is morally defensible, huge disparities in wealth tend to produce revolutions. Revolutions are undesirable.
4. Due to (3), pure capitalist markets devolve into monopolies and oligopolies, producing local maxima in the resource optimization utility function usually associated with capitalism.
All in all, anarchocapitalism is a naïve view of capitalism, where a good optimizer is mistaken as the perfect optimizer.