I might have a better analogy than the 1 million goat idea.
(By the way, I've tried this on my computer and the answer is definitely 2/3).

Most people who claim 50% seem to downplay the effect that Monty has when he shows you the goat.

Think of it this way. You make an initial guess with 1/3 probability of being right. Let's say that Monty DOES NOT open any doors, and he asks you if you want to change your guess. If this is the case, then you have a 2/3 chance that the car is behind the door you didn't pick. This 2/3 chance is spread evenly across the two doors you didn't pick, leaving 1/3 chance for each door. This is normal, right?

So why don't you switch? It's because you don't know which door to switch to, so your chances don't become any better.

Now, when Monty shows a goat, he's actually helping you out a lot. He's saying "You'd like to switch but you don't which door to switch to? Well, DON'T switch here! Now, instead of spreading your 2/3 probability over two doors, it concentrates on one door."

If this doesn't please you, here's a reasonable analysis. You can draw a tree for these possibilites. Without loss of generality, let's say that your initial guess is Door 1.
1) Let's say that Door 1 is in fact the car. This occurs with a 1/3 chance. Monty picks one of the other two doors, each with 1/2 probability (so the chance that of both you being right and him picking Door 2 is 1/3*1/2=1/6; same for Door 3). In each of these cases, you should stay. Thus, you should stay for 1/6+1/6=1/3 of the games.
2) Let's say that Door 1 is NOT the car. This happens 2/3 of the time. Monty's choice of door is forced. You should switch 2/3 of the time.

And by the way, don't get so damn annoyed at other people's arguments. I used to think as you do, but then I realized that my two apparent choices were actually not equal.