The choice to switch is a separate choice than the original choice between three doors.

The whole problem is a case of someone trying to be a lot more clever than they are.

Look at it this way:

There are three marbles in a bag, a winning red and two losing blues. As you reach you hand in and grab a marble, and before you retract you hand, you are stopped. The host looks in and pulls out a blue marble and tosses it out. The host ask if you want the marble in your hand or the one in the bag.

Simple probability kicks in. There are now 2 choices, one is the desired outcome. It's a 50/50.

Now this works all the way up until you consider the human aspect in the problem. Why is the host giving you the option to switch? If they wanted you to lose, yours is likely correct and they want you to switch. If they wanted you to win, switching is the best option. If they just want to add drama for the viewers, it's still 50/50.