Reason No. 1 - Territory
Even though you may need to close a door to go to the bathroom, to go into your bedroom or your kitchen, what you might be missing is that the door effectively interrupts access to a part of the cat's territory.
Reason No. 2 - Curiosity
You've closed the door and the cat is left on the other side. But there's a noise or a smell coming from the other side and your cat can't go over there to investigate, which means that there is a problem.
Reason No. 3 - Clowder Rule
When one or more members of the family are on the other side of a closed door, the cat can't see them, which is a problem. The meowing, scratching, and fidgeting simply means that the cat wants to make sure that everybody is alright.
How Cats Protest Closed Doors1. Meowing
As soon as the door closes, the cat becomes alarmed and it becomes vocal. They usually go sit in front of the closed door and meow and meow until somebody finally opens it for them.
How Cats Protest Closed Doors2. Fidgeting
They've meowed and meowed, but the door has yet to open, so the cats become restless and they start to fidget. They walk back and forth to the closed door, planning their next steps.