I had to think about this fuckin' problem all day (not because I had to for work, really, but rather because there was not much to do). The logic that made me finally "get it" was by re-imagining the same example but using not 3 doors, but 100 doors.

You pick a door. Your odds of being right are 1/100.
98 doors are revealed to be wrong -- all but the door you picked, and one other door.
There are now only two doors left. But do you have a 50% chance of survival if you stick with the door you picked? No! In fact, most likely the door you initially picked was wrong, and the other door is one with the elven chainmail. Your odds that the door you initially picked was the right one, is STILL 1%.

It's the same shit when there are three doors. Your chances of guessing right out of three doors is 1/3. The same probability holds after one of the death doors is revealed.

It is non-un-counterintuitive as fuck, but I had to finally grudgingly admit it made sense. Apparently it was this huge deal back in the '90s (when the Demmycrats were in charge, and that was the biggest problem America had): behold the Monty Hall debate!

Moral of the story: It's always better to switch. With doors, as with genders that you have sex with. Fuckers sex partners!