What's wrong with property?
The thing about "property" that I find most objectionable is that the idea is used to justify violence. Violence is framed in terms of self-defense when a person decides to assert property rights on an external object.
When the argument is made that idea of property has its basis in so called "self-ownership," an abstraction is created from the right to defend one's personal integrity. That single aspect of the complex relationship between me and my self is divorced of its context and applied to external objects.
We have to ask ourselves: what purpose does this serve?
The new concept that has been created is presented as the justification to say "If I catch you using that thing, I have the right to respond with violence just as if you were trying to kill me"
Clearly you have the right to defend your brother if he is being attacked. But you don't own him, and it would be a rather silly argument to make that you do. Or even your neighbor, for that matter. You don't own your neighbor, but that shouldn't stop you from coming to his defense.
Since the concept isn't necessary to justify defending another person, no case can be made that it is necessary to justify one's right to defend themselves.
What it is necessary for, is to provide cover for those who want to assert a claim to an external object, and who want to defend that claim with violence or intimidation. Almost invariably, those who argue for such rights wish to see them extend to things ever further removed from their own bodies... Such as fields and factories.
At a certain point it becomes impossible to personally defend said "property." What happens then?
At this point, I suppose it's time to start thinking about private defense agencies. The property owner must be able to call upon armed men to come assert his claim on the property.
At what point are we going to admit that this is starting to look a lot like the state that we originally decried?