You would own the home you live in or the car you drive. Those would be your personal property. But you cannot own multiple homes that you rent out. Or a fleet of cars that you run a ride share company with. Thats private property and (private)property is theft. No one wants your toothbrush, but they do want the toothbrush factory

>what about violent communities

Anarchists are not liberals. We believe in armed Resistance and fighting back. Google the CNT-FIA, the EZLN, the YPG, and The Revolutionary Insurrectionary Army of Ukraine