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.
Off topic, but I'd be interested to learn more about this police force because it's not something I've previously heard about. I know that the Generalidad de Cataluna (the Trotskyist and Communist government in Barcelona, which the anarchists broadly supported) maintained the Civil Guard, and that after the PSUC (Communists) gained increasing power just before the 1937 May Days they brought in Assault Guards (to suppress first the Trotskyist POUM, and then the anarchist CNT/FAI), but so far as I know the only police were government police. And all of the militias - from CNT/FAI and POUM militias though to the International Brigades and other Communist militias - they all were armed, they all had the right to use force, so I'm not sure I understand "exclusive privileges to use violence" - the Spanish Republic was in the midst of a civil war against Fascism - the Republic in general, and the Generalidad in particular, all condoned widespread arming of the population.