I listen to sad songs when I'm happy and it makes me sad. LOL. I don't know I guess. For me I think it's because I can relate to the sad song. When I'm upset about my brothers, I always listen to 5FDP's song Remember Everything. And every time, it just lets me know I'm not alone.
It just depends on the person and the situation. Some people, it helps them process, identify with, and let go of what they're going through. Others, they just kike to keep feeling miserable, and feel sorry for themselves.