When shooting off a rest or off the shelf, right wing or left wing doesn't matter.
When shooting a bow with no rest or no shelf, where the arrow is sitting on the hand, a right handed shooter would use left wing and a left handed shooter would use right wing. This is to angle the leading end of the feather off the knuckle to keep from getting feather cuts on the hand. If that leading end comes loose and is sticking up when you shoot... Well, let's just say pain doesn't contribute to good accuracy.
