The English description on that page doesn’t make it easy to understand what this key does. ”Its name comes from the fact that it has two key blades (the part which activates the bolt) at each end of the key, rather than the usual single blade” How does that lead to the name “Berlin key” or either of the German names? I would guess “Berlin key” comes from the fact that it predominantly is used in Berlin. ”After unloc…
1. You can only remove the key if it is locked. 2. You can't lock it unless the door is closed.
That ensures that when you have the key then the door must be locked and closed.
The think about pushing the key through they door is just because otherwise you have no way to start inside the room, unlock and open the door, and then lock it behind you. Remember while the door is unlocked you can't remove the key. So if you just go outside and shut the door the key is now inside... and the only solution is to pull (or push) the key through to the door to the outside. Then you can lock the door and remove the key.