Private property goes pari passu with the state, more specifically with its laws. No state, no private property, because in the wild might is right: if someone stronger than you points at your property and says "that is mine" you can't do nothing but obey or be deprived coercively.
I could easily pay someone even stronger to protect my private property. Doesn't have to be state, does it?
But then they control the property, not you. You can call it yours if you want, but it really isn't.
If someone built an army strong enough to protect your property from any threat out there, they're not going to give a flying fluck about your claim to that property. This is why conventional anarchists are opposed to private property. The result is pretty much the same, but at least they see the problem.
BTW, could the price stop rallying? I'm having trouble posting this thing when everyone get so excited.