It's kind of confusing but easier to understand when you consider the primary goal which is to force people to lock the door. This is achieved by only allowin

It's kind of confusing but easier to understand when you consider the primary goal which is to force people to lock the door. This is achieved by only allowing the key to be inserted or removed when it's in the locked position. The push through is to allow them to lock the door on either side. 1: it's a key that can only be inserted or removed when in the locked position. 2: It can be only be pushed from one side to the other when in the unlocked position Therefore you can unlock the door on one side to let someone in, lock the door on the same side and remove your key again. Alternatively you can unlock the door then push the key to the other side, lock the door on the other side and remove your key.