Appeal to spite (also called argumentum ad odium) is a logical fallacy in which someone attempts to win favor for their argument by exploiting existing feelings of bitterness or spite in the opposing party.

For example:

"By voting for my proposal instead of Jim's, you'll finally have a chance to get back at him for running over your dog!"

"Bill Gates dumped you in highschool. Therefore you should never buy any Microsoft products."

Spite can often be taken to illogical extremes, and result in very poor decisions. The classic phrase "cutting off the nose to spite the face" is an example of flawed, spiteful logic.