When we got our puppy years ago, we hung a string of bells on the door and taught her to "ring" when she needed to go out. Worked great! Then last year we rehomed a cat. It didn't take the cat long to figure out the purpose of the bells. He would ring the bells, then hide near the door while the dog would dutifully, but with a very confused look, head for the door to go out. Prince would then saunter out of his hidey hole looking very proud of himself for ridding us of the pest.

Smart kitty, hiding kitty, little ball of fur.
Happy kitty, tricky kitty, purr purr purr.

are why I prefer cats

The dog trained them, because in the new place they respond to any door-licking as a signal and let him out. This reinforces his behavior.

Smarter owners (sorry to have to say this) would discourage the licking of random doors, and encourage only the desired behavior.

Dogs are trainable.