Please don't conflate "anarcho"-capitalism with anarchism.
If you'd like to learn about anarchism, even for the sake of improving your arguments, I'd recommend
An Anarchist FAQ.
To smash private property, you need a state. Capitalism, on the other hand, exists independent of the state. Given what happened in Spain, where the first thing the so-called "anarchists" did was set up a police force with exclusive privileges to use violence, nobody buys the socialist "anarchist" line anymore.