I think that everyone has the power to be wrong, but to be very wrong with convincing arguments, you must be smart.

A smart person can come up with post-hoc rationalizations that hold up under some scrutiny, to the point it is very hard to convince them otherwise. Add to that people who became famous or successful on the back of "being right" on some subject matter, getting used to "being right even in the face of overwhelming push back", and you have a recipe for very smart people being very wrong in very visible/loud ways.