You confused yourself. There are four possible outcomes at the end, but they are not equally likely. So not 50/50.

If Monty always shows a goat, it is undeniably a 2/3 chance to win on switch.

The nuance here being discussed is whether you can assume Monty would have shown you the goat had you chosen a different initial door just because he showed you one this time. If you don’t know that, then you don’t learn anything.

Edit: actually I misread. You just chose to ignore the cases where Monty revealed a car. Which is correct although most people chalk that up as a win or loss.