The explanation is correct if, but only if, the host is required by the rules of the game, which are known to the contestant, to show the contestant an empty door no matter what door the contestant first chooses. For some reason, statements of the game never seem to mention this detail. What if the host only shows the empty door if the contestant chooses the one the host knows has a car behind it, making some other offer if there's nothing behind the chosen door? If the contestant doesn't know all the rules governing the game, the contestant has no way of knowing the right move statistically.