The framing that made it click for me was to instead offer 100 doors and, after the contestant picks one, have the host open 98 of them and then give the offer to switch.
Alice is right handed, Charlie is left handed. Bob is looking at Charlie, Alice is looking at Bob (and does not see Charlie). Is a right handed person looking at a left handed person?
”Maybe Bob is ambidextrous” is a good unintended answer.
The framing that made it click for me was to instead offer 100 doors and, after the contestant picks one, have the host open 98 of them and then give the offer to switch.