Appeal to spite

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

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.

See also: Appeal to spite, Cutting off the nose to spite the face, Logical fallacy