And now I know the name for this. (via)
The Forer effect (also called the Barnum Effect after P.T. Barnum’s observation that “we’ve got something for everyone”) is the observation that individuals will give high accuracy ratings to descriptions of their personality that supposedly are tailored specifically for them, but are in fact vague and general enough to apply to a wide range of people. This effect can provide a partial explanation for the widespread acceptance of some beliefs and practices, such as astrology, fortune telling, and some types of personality tests.