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Mom is irritating her son. The definition of irritate is to aggravate or annoy, or to cause itchiness, inflammation or discomfort in or on the body. When you annoy someone, this is an example of a time when youirritate them.
To antagonize is to provoke someone to react angrily. If your mother tells you to stop antagonizing your brother, she's asking you to stop making him mad. Antagonize shares the same Greek roots with the word agony, so think about how much agony you cause your siblings when you tease and goad them into getting angry. Bugs Bunny is known to antagonize Elmer Fudd, who hunts but never does catch that wabbit.