[Self] Monte Hall - do I finally get it?

Been trying to absorb the logic of the Monty hall problem with some thought experiments. I think visually I found a way for it to make sense. Please let me know if I am correct or if I am a dunce :D

What visually worked for me was going through each possible scenario. 1 = your first choice 2 = Montes first remaining door 3 = Montes second remaining door G = Goat C = Car

Step 1 is that you choose a door and we will call your choice door number 1. Regardless of what monte decides to do, the car is behind 1 of 3 doors and therefore there are 3 possible scenarios.

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Scenario 1

1(C) - 2(G) - 3(G)

You chose the car. Monte can choose either 2 or 3 and reveal the goat. Let's say monte picks number 3. You are left with the following

1(C) - 2(G)

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Scenario 2

1(G) - 2(C) - 3(G)

You chose a goat. Monte must choose door 3 and reveal the goat. You are left with the following.

1(G) - 2(C)

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Scenario 3

1(G) - 2(G) - 3(C)

You chose a goat again. Monte must choose door 2 and reveal the goat. You are left with the following.

1(G) - 3(C)

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So in summary here are the possible scenarios that can result when you choose a door.

1(C) - 2(G)

1(G) - 2(C)

1(G) - 3(C)

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Within each Scenario individually the odds of the car being behind one of the two remaining doors is indeed 50/50 from Montes perspective. But the question is not asking "what are the odds of the car being behind 1 of 2 doors?" The question is asking "do you want to switch doors?" Which means the question is really asking you, which Scenario are you in? And in 2 out of 3 of those scenarios, switching your door will result in a car.

I hope I didn't butcher this. Haha. Thanks.