Interesting point but I think there is a fine line between responsibility and "ownership". I felt it was a little more than just my responsibility for what my children did when they were in our household. Most people refer to their children as "my" daughter or son - that implies the concept of ownership. However, I agree that all life is the "property" of our Source, God.
There’s no fine line at all. There is a bright clear line.
My child is my responsibility. My dog is my property.
I can shoot my dog.