The only comment I'll make, is that being clear with definitions and which part of a definition you disagree with is helpful to discussions. I agree that private property is a superset of personal property. But in your response you didn't introduce the distinction nor explain the part of the definition you find antithetical to liberty. I think most people wouldn't know the different definitions and would have a knee jerk reaction to what you are saying, potentially interpreting your statement more strongly than you intend. Unless you intend to say you find individual ownership of toothbrushes antithetical to liberty.
That's all. Have a great day!