The bathroom can have one of two situations, with two states that go hand-in-hand with each other:
No other combination is possible — the door can't be locked with nobody in the room (how would we unlock it?), and the door can't be unlocked with someone in the room (how would they ensure their privacy?). This is an example of a semaphore with a count of one — there can be at most only one person in that room, or one thread using the semaphore.
The key here (pardon the pun) is the way we characterize the lock. In your typical bathroom lock, you can lock and unlock it only from the inside — there's no outside-accessible key. Effectively, this means that ownership of the mutex is an atomic operation — there's no chance that while you're in the process of getting the mutex some other thread will get it, with the result that you both own the mutex. In our house analogy this is less apparent, because humans are just so much smarter than ones and zeros.
What we need for the kitchen is a different type of lock.