You can say 'simple' but a whole pantheon of academics famously got it wrong. If you really want to understand the problem use 100 doors instead of three and then it becomes very clear whats going on.
I also don't think changing the problem to an analogous one is as helpful as this direct and simple solution. Using 100 doors could mean multiple things. Maybe it means at the next stage you have 99 doors left. Maybe it means at the next stage you have 2 doors left. Why should I think either is the correct analog? You can just see the simple answer I've stated and be done with it.