Gripping the ring is what causes it to distort and jam more tightly, so the clue is to find a method to apply force evenly and lightly around the whole ring then turn it.

Another method is to apply force to the front of the ring rather than the outside. You can do this by stretching a damp dishcloth over a smooth tabletop, then push the offending ring face down on the cloth, apply a bit of force downward and turn. Good luck!