It's an almost universal behavior across our feline friends. Your cat sits at the door, meowing for someone to open it, and then you open it, let the cat in, and then close the door again. Then it's immediately meowing for someone to open it again.
Why? It's because cats are territorial and hate closed doors.
When cats are meowing or pawing at a door, they more often than not are asking you to open the door and leave it open.
They might not want to go outside (or inside) the room, but they prefer not to have any of their territory blocked off. If you let them through and close it again, they'll often just do the same routine from the other side of the door no matter which side you put them on.
Because of their territorial nature, cats believe they actually OWN your house. When you close a door, it is no wonder that many cats will try to open, scratch, or attack it in every single way. They may simply find your attempt to close a door as a sign that undermines their absolute reign of the territory.
Here's a video you might like: A cat owner tried to prevent his cat from opening his bedroom door by placing a large bucket of water in front of the door - but the cat's determination is far too strong.