I don't think possession is a simple black and white thing - when we say that "this is mine" it can indicate a whole range of relationships between us and whatever it is we are dealing with. A stick, a house, a painting, a song, a country, a husband or wife, a child.

In that list the only absolute possession is the stick - I mean that is the only case where we have a free moral right to dispose of it as we like, and destroy it if we choose. (And I can imagine cases where even thta "right" is not absolute.) Most of the the words "my" and "mine" imply some kind of duty of care.