To chafe is to irritate or annoy. If your shoes chafe you, they rub your skin raw. Ouch. If you chafe at the suggestion that you should be studying more, the suggestion rubs you the wrong way.
Chafe originally meant to warm, like a chafing dish on a hotel buffet. Though this may seem like a big jump, think of when your hands are cold and you rub them together to warm them up. So you can say that rubbed skin is kind of hot as is a temper flaring up from irritation. If you are a hot head, you are easily chafed.