So I've self-identified with anarchism (more specifically council communism)

Thats not anarchism.

Let's say there was someone who didn't agree with communal ownership and wanted to create private property.

To set up private property relations you have to take what people currently consider to be public, ring fence it, deny people access and demand rent. How are you proposing someone does that? If you tried people would turn round and tell you to screw right off, you'd have to bribe them with something and rely on them being foolish enough to have forgotten what private property is and fall for that shit. And what the hell are you bribing them with? We can look to history and see where private property stems from, and it comes from violence, and armed state declaring its ownership of land, ringfencing it, giving deeds of ownership to some and demanding rent and taxation from others who happen to live there. So when you say what if someone wanted to create private property i'd be quite justified in turning round and asking "them and what army"