Take it to the extreme. Say there are 1 million doors, and only one has the prize. You choose your one door, and save it for later.

Now the host eliminates all the other doors but one. *All* the opened doors are for jelly-of-the-month.

So there are two doors left. The one you picked out of 1 million, and the one the host choose for you. It would be foolish not to switch, no?