A puzzle

[FlawlessHappiness]

I have no doubt in your drawing. The math behind it is 100% correct.
What I don't like about this problem is the wording of the solution.

He just remove that wrong door. Your chance is still 1/3.

How can the chance still be 1/3 if there are only 2 doors?

You would have 50/50 when you would mix the two remaining doors and pick again.

Which is the end result. No matter whether one door was removed or not, you are "mixing" the two doors and picking again.
"Mixing" here is by not mixing them. You still don't know what's behind the doors, so whether they're mixed or not won't matter.