Labeling stuff with "My" imitates the point of view of the user. It is as if the user has printed out labels and stuck them to various objects: My Lunch, My Desk, My Red Stapler. Except the user hasn't done this; you (the site) did it for them.
Labeling stuff with "Your" instead reinforces the conversational dialogue. It is how another human being might address you when talking about your stuff. Even with MySpace, people say things like "I saw what you put on your MySpace."
