Ok, I thought about this long and hard. Originally I thought that the answer was that there is no difference between switching or not. I was wrong, and here is how I now understand it.

First you have to understand the question:
"is it better to switch, or does it not make a difference if you switch"

Then you have to understand the situation:
2 Stages
Stage one: 33% chance of picking correctly
Stage two: 50% chance of picking correctly

Then you have to understand that little tiny bit of often overlooked information, the key to understanding the answer:

The door you picked in stage one is probably wrong. You know this because the probability is 33% during stage one. If you don't understand this key point re-read it until it has sunk in. You probably CHOSE WRONG. This is key.

Since you are in stage two, here is your choice:

- stick with the door you have picked (which is probably wrong)

- switch to the other door