[upofadown]

> that pilots are most definitely taught that pushing forward (up) on the yoke causes the plane to dive (go down),

No, they are taught that pushing forward on the yoke causes the nose of the plane to pitch towards their feet. The result of that depends on the starting attitude of the aircraft. Think inverted flight as an extreme example. In exactly the same way, pushing on the right handlebar has results entirely dependent on the starting attitude of the bike.

Your comment about the roll is correct. That is an effect of a control.