We're not sure about this one, but there are two competing schools of thought:
1. "Ripping" was original used by early-generation computer hackers in the Commodore 64 era (mid-'80s) who would "rip" images or audio files out of games to use elsewhere sort of like ripping a page out of a magazine to hang on your locker door. Getting this data out of a game program would usually require serious computer know-how and might occasionally skirt legality. Today's CD ripping (or digital audio extraction) is easy and generally legal, but is a similar activity.
2. "Ripping" is short for "ripping off" because you are stealing music that belongs to the CD.
I think the first one is probably closer to the truth.
See: The Egge Adventure