After all, if someone you know is planning to quit her job and move to Alaska because her horoscope told her that Tauruses need more spontaneity, you shouldn't tell her to stay because she's actually an Aries.

This seems just plain wrong. If "winning" is "getting her not to quit and move to Alaska," pointing out this error seems like a very rational approach; I would even call it the most rational obvious solution. You could, then, conceivably use this error to make a greater point about the problems with astrology as a belief system. But if your immediate goal is stopping the move, giving someone who already strongly believes in astrology a lecture on epistemology is not a winning proposition.