I could not resist - I did not believe the supposed right answer, so I wrote a quickie computer simulation and tested it over many, many iterations. Switch was the right call two-thirds of the time. Once I looked more closely at my code, it became obvious why.
The contestant makes a pick. His chances are one in three of it being the right one. That means the chances are two-in three of it being the wrong one. So, the contestant is shown that one of the doors he didn't pick is a loser. The odds of his original pick remain - one in three. That means that the other unopened door has a two-in-three chance of being the winner. The computer simulation confirms that this ratio is close the results it produces.