The problem with your argument is, of course, that you presume there is private ownership of property, but neglect to specify how that ownership originated.

Absent the threat of violent force against anyone who does not obey conventions with respect to ownership, there is no such thing as ownership. So in order to have even the concept of private property and "rights" thereto you must postulate some entity which recognizes those "rights" and will enact violence on your behalf against certain classes of others who would "violate" them.