This always bugged me. It isn't switching your choice that gives the 2/3 probability, it is exercising a choice once one of the doors has been eliminated. The odds are the same as flipping a fair coin to decide on which of the two doors remaining to pick.

Am I wrong?

Yes.

You pick a door. Probability 1/3 it has the car behind it. The host then picks another door, revealing the booby prize. That door now has probability 0 of having the car. But you still picked a door with probability 1/3 of having the car, which means there's a 2/3 chance the other door you didn't pick has the car. Write a program to run a Monte Carlo simulation... of the Monty Hall problem... and you will see this is the case.

The host has given you information about where the car is by revealing where it is not. Whether you can effectively use that information is another matter.