It's probably the idiotic "secondary latch" that GM - AND NOBODY ELSE EVER - put on their spare tire carriers for some dumb reason. With the secondary latch, even if you were to cut the cable completely, the spare would still be hanging up there. The Secondary latch is supposed to release when you press up on the spare, but given their location they very often rust solid. Mine was completely rusted in the "locked" position.
Anyway, what I did was got an angle grinder and ground off one of the "ears" of the bell-shaped part that goes through the center hole of the spare wheel.
Once you do that (be ready to catch the spare tire when it falls!) you can remove the rest of the mechanism with a couple of bolts.
Also, if you want to, you can replace the hoist with one that doesn't feature the secondary latch.
Too bad Photobucket went Full Retard, I had all the photos of this on there. Still have them on my computer but no way to post up here.