Heyday is what you mean, I think.

There are 2 choices so they are equally likely

There are only two options at that point. It MUST be 50-50.

The host’s intentions are irrelevant. Numerically, there are only two choices. That makes it fifty-fifty.

Now you have 2 choices: the door you chose, or the only other door left. One has a goat and one has a car. That’s fifty-fifty.

In your explanation, the door originally had a 1% chance, but after showing 98 goats, it has a 50% chance.

After you find out there’s a goat behind door #2, you have a 50% chance whether you stay on 1 or move to three. There are only two possible outcomes at that point (car or goat), so either way it’s a coin flip.