Bryan Caplan debates Yaron Brook on anarcho-capitalism. You can safely skip Yaron’s parts, but Bryan’s part are golden.
Rothbard.com
Murray Rothbard, Libertarianism, and Anarcho-Capitalism
Bryan Caplan debates Yaron Brook on anarcho-capitalism. You can safely skip Yaron’s parts, but Bryan’s part are golden.
Rothbard.com 
Here is an argument against anarcho-capitalism:
Ancaps support NAP, which states that actions caused by initiated aggression are immoral. By extension, every market that is based on initiated aggression is not a free market. Here is the problem:
In the standard Ancap view, it is the private protection agencies (PDAs) that protect people from aggression. Basically, a private protection market is formed. But the reason why people take part in this market is the credible threat of initiated aggression (i.e one is afraid of being robbed, killed, etc.). But if we review NAP, then this is not a free market, since it exists solely due to the presence of initiated force. In short: Anarcho-capitalism contradicts its own philosophy.