I think the part that makes the right answer (i.e., always switching) counter-intutitive is the fact that two of the possibilities are being collapsed into one.

If you choose a goat initially, there is only one door the host is allowed to show you. (He'll never show you the car.) That creates two cases of pick-show-switch. Two wins.

If you choose the car initially, he can choose either of the other doors to show you. People are considering that situation as one scenario, rather than two. We should consider pick-show the first goat-switch and pick-show the other goat-switch. Two losses.