So the hero has a chance to kill the Big Bad, or some other villain, and the villain wants them to take it. He goads the hero into doing so. Often it's because My Death Is Just the Beginning, or the villain is invoking If You Kill Him, You Will Be Just Like Him! and wants to push the hero off the Slippery Slope like The Corrupter.
This is often more than a Thanatos Gambit — the villain doesn't necessarily intend to die. In these cases it's enough that they provoke the hero into making the attempt. Once the hero has turned on them with intent to murder, the villain has already proven their point.
The other times, the villain really does want to die, but they can't, so they goad the hero into killing them. After which they explain their true motive.
Whether this works or not depends largely on the Sliding Scale of Idealism Versus Cynicism, but it does make for great dramatic tension no matter what. Heck, at least part of the time, the villain is taunting the hero because they know he won't do it. This also means that the success or failure of this gambit hinges on whether or not the hero has any preexisting qualms about killing. Said villain might try this on an Anti-Hero (especially with more extreme cases) and get his ass handed to him, due to the hero's lack of such moral restraints. This could then lead to Hero with Bad Publicity because he lacks such restraints; who looks like the aggressor in this situation?
This can easily backfire if the hero realizes what the villain is trying to trick him into doing precisely because of the evil gloating. It may also backfire if the hero counters this with Not Worth Killing or Cruel Mercy.
It can overlap with What You Are in the Dark. Compare with The Power of Hate which is a focus of the power hate gives. Contrast Get It Over With. The villain may employ taunts like pushing the Relative Button, Reminiscing About Your Victims, or asking Would You Like to Hear How They Died? in order to get the hero to strike. Inverted by Turn the Other Cheek, when the hero makes themselves vulnerable to appeal to the villain's better nature.
Of course, there are occasions where the hero does strike the villain with all of their hatred, yet the hero realizes that it's the only way they can feel better and cleanse their hate, simply because, to them, Revenge Is Sweet and they could care less about their moral codes.
