1. Empirical Argument:

Capitalism is a societal order that currently exists in several countries.

Anarchism is a theoretical societal order that does not nor did not exist in any country that could also be described as capitalist at the same time.

2. Theoretical/Pricincipled Argument:

For Capitalism to function it requires the following concepts to be mutually agreed upon and accepted by ALL parties who wish to participate in capitalism:

a) concept of private property

b) common concept of capital or form of exchange (i.e. money)

Because those things have to be common among all capitalist participants there has to be a common authority to protect and enforce them which is antithesis of anarchism. Hence the two are incompatible.

3. Philosophical argument:

Just as in debate of weather the God exist or not. The side that purports to know the existence of God shoulders the responsibility for any evidence or proof, so is in this argument side that sais that Anarcho-capitalism CAN or DOES exist shoulders responsibility for proof. My side is content with the fact that historically the two forms of social organization have not coexisted together. So you can still believe in Anarcho-capitalism just like you can still believe in God.

4. Common sense argument

Just imagine doing business with an anarchist who thinks property is theft.