A harpy is a mean, foul-tempered woman. You might quietly refer to your cranky math teacher as a harpy.
The word harpy is a derogatory term for a very unpleasant female person. It is often considered offensive to call someone a harpy, in part because it singles out a nasty woman, when a man with similar characteristics might simply be "loud" or "opinionated" or "overbearing." The word comes from Greek mythology, in which a harpy was a food-stealing creature with a woman's head and the body of a bird.