Adding to the previous discussions on counter-steering bicycles: you can see it in tyre tracks. e.g. ride through a puddle; or, ride from rain to under cover.

Consider: how do you steer riding no-hands? Shifting your body weight makes the front wheel turn (because of the "rake"), but now your bodyweight is on the outer side of the turn! Hold it for a (brief!) moment, then lean the bicycle the other way and you have a nice turn in the opposite direction - which is what you wanted all along.