Hi, thanks for testing! When you pick up a key, it opens one access point but closes another. So when you pick up the initial key, it closes one access point but automatically opens another.
At the beginning, you have access to the library room, which is at the top of the spawn point, and when you take the key, it closes that access point but opens another one.
Sorry, this isn't very intuitive; I think it's a communication issue on my part.