Maybe this example will help. It's always easier when there's more than just three doors.
Lets say there are 25 cases. One of them has $1,000,000 in them, all of the rest have nothing.
The host says "pick one case." You pick your case. Now there are 24 cases left.
The host takes away 23 cases, all of which have $0 in them (this was predetermined, there's no way that the host could've eliminated the $1,000,000, he is going to eliminate 23 $0 cases each time). Now there's the one you picked, and the other one. The host says "would you like to keep the case that you picked, or switch?" That's not 50/50, that's the host essentially "giving" you the $1,000,000 case, unless you happened to pick it right the first time, which is quite unlikely (only a 4% chance).
Basically, the host has said, "if you were right, you have the million dollars. If you were wrong, I am showing you the remaining case that has the million dollars. Do you think you were right?"
You can make this even more absurd. Let's say you're picking powerball numbers. You pick your number. Then, a genie comes and says "I have eliminated every other set of numbers that isn't correct. If you picked the right numbers the first time, the numbers in my pocket are nonsense. If you picked the wrong numbers the first time, the numbers in my pocket are correct." You'd never assume you picked correctly, that there's a 50/50 chance you have the right numbers, you'd know there's an absurdly small chance that you picked correctly, and you'd graciously thank the genie for giving you the correct numbers. This is the same thing, just with a LOT higher odds, and a LOT more eliminated wrong answers.
I suppose a tl;dr version of the original problem would be, "if you originally picked wrong, the host is essentially GIVING you which of the other two doors have the car." It's easy to see with 25 cases, the host automatically changes the odds for you, essentially GIVING you the winning case (unless you happened to pick right the first time).
The original problem is the same thing, just with less absurd odds. Lets say he didn't "reveal" the donkey, but instead phrased it like this. "You have picked a door. If you are right, you have the car. If you are wrong, I will tell you right now that the car is in door B." Now, all of the sudden, you have increased your odds. You've essentially changed it, so that if you switch, you've picked BOTH B AND C, because he revealed exactly where the car is, UNLESS you're right. Just like, with 25 cases, he took away all of the other wrong answers, so that you essentially win the $1,000,000 UNLESS you picked the $1,000,000 the first time.
