Diagnosis
The detent ball and spring in the anvil are jammed with dirt or the socket is corroded on.
How to Fix It
Apply a drop of penetrating oil (like WD-40) where the socket meets the anvil. Let it soak for a minute. Grip the socket firmly with channel locks or a vise (protect the socket) and pull straight off while wiggling slightly.
If That Didn't Work
The detent ball may be seized. Use a small pick to try and depress the ball through the hole in the socket drive. This may free it.
Heads Up
Do not hammer on the anvil. You can damage the hammer mechanism and warp the anvil. Never heat the anvil with a torch.