Jason, you suffer from a delusion known as "reality" - mathematics isn't about reality by its very nature. Having two options doesn't mean that there's a 50/50 chance that either is right. In the real world, it does. Not in math games, though.
This is the folly of the explanations typically given:
the probability involving the two real items behind the final choices isn't the same thing as the probability of picking the correct door. You're not influencing the probability of the doors themselves, you're influencing the probability of choosing a door. Shit, that didn't come out like I wanted it to. Let's keep going - One door is more equal than the other. Your problem is that you think the 1/2 probability of what's behind the doors is the percentage in use. It's not. It's secondary.
Your initial "uninformed"decision to pick a door gives you a one in three shot at getting it right. The unveiling of the goat doesn't change what's behind the doors, yes. There's still a goat, and still a car. The idea that you are betting on the objects is a logical fallacy. You are betting on the likelihood that the door you initially chose was correct. You have to go at this in a pure math (rather, theoretical) sense. The initial probability IS one third. You are impartial to every variable that might influence your initial choice. After the first goat door is shown, you are betting not that the likelihood of one door holding the car is greater than the other, but that your choice is now more informed than your initial one. The probability, if going at those two doors without any past experience in the matter, that you get the car is 1/2. Not the case if you started with three doors. Your choosing of door A actually *changes* the likelihood of that door holding the car, mathematically. How's that for chaos theory, eh?
Now, these numbers that people are throwing around for percentages *are not* case by case numbers. Going back to what I said earlier - if you have a single run at a percentages game, the mathematical values and possibilities will likely seem less apparent in the outcome than if you played that same percentages game 500 times. Making the switch in this game isn't particularly influential if you're only going one round. Ever flip a coin and keep landing on the same side? This stat stuff isn't that reliable for small numbers. You could play this game several times, and the benefit of switching versus not switching wouldn't make itself apparent to you. However, in general it does increase the likelihood of winning the prize.
As you can see, I'm not the greatest teacher. I do understand the math behind, though, but my difficulty lies in representing the outcome in non-math terms. I hope this makes sense to you. If you don't think the first part I mainly scratched doesn't meld with the second part, clear it from your mind. My wording wasn't accurate.