Ordinary people are going to be thinking about a key in a lock. Does the lock on your house store the key inside? Maybe in some kind of information-theoretic sense but in the ordinary meaning of the word, no, it has a representation (that may not even be sufficiently specific to recover your key exactly). And if you lose your key you don't break into the lock to recover it--you call a locksmith to replace the lock, and get new keys.
That right there is an intuitive understanding of both hashing and good security principles that goes surprisingly far.