Your first choice is random, and is probably wrong for the reasons already explained.

The host's choice of door isn't random. He knows where the car is, and he knows which door you've picked, so he opens a different door which will always reveal a goat.

That leaves a choice between two doors. Your first choice was probably wrong, so the other must be probably right.

It's not the same as a random choice between 2 equal doors. Which 2 out of the original 3 are left has been influenced by your first choice.