[bzbz]

And I think you stumbled upon the crux of the problem. I think we have a hard time grasping the fact that Monty not just picks one of the other two doors, but also specifically guarantees that it won't be the winning door.

Without that guarantee, it makes no difference.

Additionally, there are not many situations in real life that would replicate the conditions of that guarantee. So our "intuition" is simply geared towards situations where an actor can't read our thoughts (door pre-selection) before we act them out, and in such a scenario, pre-selecting/switching selection of doors doesn't matter.