Pirating songs is not stealing. It's copyright infringement.

If I go to the store, pick up a carton of milk with my right hand, and magically get a second carton of milk in my left hand, then walk out the store with the carton of milk in my left hand, leaving the original carton in the store, then I have not stolen anything. If that is stealing, then I can only conclude that stealing is (a)moral, and we need a different word for what I would consider to be stealing.

Piracy has been proven in court to not be stealing. I'm using the legal definition of stealing.