First, solve this related problem:
Before any of the three doors are opened, Monty says “You may either pick one door or eliminate one door and pick both of the other two doors” What is the best option?
Hopefully the answer is obvious to you. You have a 2/3 chance to win the car if you pick two doors. You have a 1/3 chance if you pick only one door.
Now consider the actual Monty Hall problem.
If you pick one door and stick with it, you have a 1/3 chance of winning.
When you switch after seeing the goat, you are eliminating only the door you originally picked so you have a 2/3 chance of winning. The only way you can lose is when the car is behind the door that you originally picked.
The Monty Hall problem is just a round about way of giving you the option of picking two doors.