It's just a grammatical construction. I'm aware of no language in which the possessive case implies legal ownership. It implies a particular relationship between concepts. In only a few instances is that relationship legal or physical ownership, and even then it's not really implied by the construction. "My dog" by itself doesn't tell us that the dog is a possession or my personal property. We know it's a possession because we know that's the normal relationship between humans and dogs, not because of the grammatical construction. We can still say "my dog" after it's been sold, stolen, or lost and is no longer owned by us. Likewise we can say "my friend" without implying ownership; otherwise "my friend" would be understood to be synonomous with "my slave." Ditto "my doctor," "my worst enemy," etc.
"My school," "my profession," "my curse," "my planet," "my obsession" - none of these imply actual ownership by me. Some can be read to mean the opposite - the object owns me.
Umm, what was the question, again?