If your parents say you're too young and irresponsible to drive, you can refute their claim by ticking off examples of your responsibility. If you refute a claim, theory, or opinion, you prove that it is wrong.
Evidence and arguments are used to refute something. So are facts. Children with a shorter school day doing well on test scores refutes the idea that longer school hours promote better learning. Refute comes from Latin refutare "to check, suppress." Near synonyms are confute and rebut. All three of these verbs can apply to a person, as in "The scholars have decisively refuted/confuted/rebutted their opponents by arguing that the theory cannot be proven."
