Gnu asks, "Please... could ANY of you explain to me why you think there are three doors?"

I'll try. It is asserted on the first round that there are three doors...because there are.

Whether the car is won by the contestant (you) is determined by two separate, but connected actions. The first action is picking a door. Your chance of picking the door with the car is 1/3. Since there are two goats available, the chance of picking a goat is 2/3. You don't win the car on the first round if you chose that door, but neither do you lose if you didn't choose that door. By rule, you will never be shown the car's door; you will be shown a goat's door; neither will you be shown the goat's door you chose. The door exposed is then taken away. You need a second action to complete the game.

Nobody is asserting there are three doors on the second round. There are two doors left. These are the same two doors that were part of the available three doors in the first round. They are in the same relative position, and the prizes are still behind the doors they were behind in the first round. The prizes are always one goat and the car. [If the car were eliminated, you would have no chance to win the car, but Monty has showed you that it is still available, because he exposed one of the goats.]

The action you need to take in the second round is to choose a door. Your choice can be your original choice, in which case you have kept your chance of winning at 1/3, because you chose only one door out of the three that were available to you for the complete game. You have simply made the same choice twice! But if you avail yourself of the chance to switch, you have then chosen 2 out of the 3 doors that were available at the beginning of the game, thereby increasing your chances to snag a car to 2/3!!

BTW, you may have a degree in Philosophy, and a Masters in Engineering, but the scion of JotSC has a PhD in Philosophy, emphasis in Logic and Linguistics. He has read this explanation, and the grid of TheSnail; he agrees with both. Actually, he wonders why the grid is not sufficient, in and of itself, to convince you of the proper probabilities and outcomes.