This is one of those things where it really isn't a matter of opinion. There is a correct answer and an incorrect answer, and yours is incorrect. One way to demonstrate that it's incorrect instead of using mathematics is to actually play the game a bunch of times, and see how often you win with the strategy of always switch.Let's work this another way.
You choose a door, Monty opens another door (big surprise no car) and offers you the chance to change doors.
If the door you are offered has a 50% chance of having the car behind it, then the door you selected must also have a 50% chance of having the car behind it. The sum of probabilities is after all 100%.
If, as supposed by so many, the door you selected has a 1/3 (33.33%) chance of having the door behind it then the sum of probabilities is 83.33%. If you believe the door that was opened also had a 1/3 (33.33%) chance of having the car behind it, then the sum of probabilities is 116.66% which is also problematic.