If we don't consider what made a person "popular", ie have many friends, this "phenomenon" just makes statistical sense to me. You have a greater chance of being in a pool of friends that is large, while your pool of Facebook friends is smaller, so out of that smaller pool you have less of a chance of one of them being less popular than you. It is already unlikely that unpopular people are one of your Facebook friends because they themselves have so few friends.

I have no mathematical proof; this is merely what I intuit.