I feel like it’s super over-explained.

You have a 1/3 chance of choosing correctly in the first place. Meaning the chance that the prize is behind one of the doors you didn’t pick is 2/3.

You then get the chance to switch to the last remaining door, after the host reveals one goat out of the two doors that were left.

Since the chance that the prize was behind one of the two doors you didn’t pick was 2/3, switching to the last remaining door after the reveal means you have a 2/3 chance of winning by switching.