The Monty Hall Problem is a great example of why our intuitions cannot be trusted when it comes to probability. If you are not familiar with the problem, the wikipedia link above gives a good description of the problem and it’s historical significance. There are examples of Ph.D’s not getting it, it’s just counterintuitive.
If you are still not sure why switching is the better strategy, I have made the following diagram that visualizes all of the possible outcomes and their probabilites.