Can't remember if it has been phrased this way, but here goes:

If the question were, what are the odds of the prize being in either one of the unopened doors, if you did not know which door was originally chosen, the correct answer is indeed 1 in 2.

This of course is not the question, and the rules and dynamics of the game materially affect which door is opened in relation to which door was intially chosen.

With the question being are you better off switching under the circumstances described, the answer is yes as the odds are 2 in 3. Another way to put it is what are the odds of the prize being in the CHOSEN door, the answer to that being 1 in 3--just as it was in the beginning when the initial choice was made.