[spronkey]

My theory on why it's such a difficult problem to understand is that it's too easy to get caught up in the real world problem, when this isn't actually a real world problem.

In the "real world" problem there are additional variables to consider, such as whether or not the host would open a door containing a car, whether that would result in a win or a loss, whether the host would offer a switch in all cases, whether if so, there is any additional incentive for switching (which wouldn't adjust the probability of winning, so is a red herring, but "intuitively" it seems that if the host is trying to make you lose by trying to make you switch, probability should go down).

When you try to conflate the real world problem, which actually has multiple different probabilities depending on exact scenario, into an answer to what's generally accepted as the "Monty Hall Problem", some of this gets in the way.

In addition, there are two probabilities in the "Monty Hall Problem" - the first is whether your switch results in a win. The second is the probability that, if you switch, it was the correct choice.