There's a very easy way to convince all the doubters.
Take three upturned cups and a small object that each cup can conceal underneath.
Ask a family member to act the part of Monty Hall, i.e. to hide the object underneath one of the cups (without you seeing), and, after you've made your first choice, to lift a cup that doesn't conceal the object. Then you make your swap decision, and then you see which cup conceals the object.
Do this about thirty times, and see how often the object appears under each cup. Unless one of you cheats, I expect that it will be about 10 times under each one.
If you believe that the probability that we're all debating is 50:50, and if you're right, then the object will be under the cup that you first chose about 15 times, instead of about 10.