Originally Posted by pretbek
The biggest deal to me is people knowing that they push left to go left, push right to go right.
After that it is your choice how conscious you keep it in your everyday riding.
Against the "just ride" argument are the cases where people have been getting by for many years with steering by "leaning I that direction" (causing them to push-steer without knowing it). That works right up until the time that you need to maneuver really drastically. No amount of leaning is going to save you then.
THAT is when you need to know that you push hard to go in that direction.
But you don't need the physics definitions and all the calculations now, do you.
You know the learning process curve is significantly raised when a rider rides a bit more aggressively and usually starting on a small/midsize bike where you have to ride like that to keep up. They tend to gain, because they have to. It wasn't easy keeping up with those Z1s with my S3 (900 four stroke vs 400 two stroke), so I learned to ride a bit harder to keep up and pretty soon I was leading when in tighter winding roads where the horsepower didn't come in quite so handy.
That and the key point that the OP already realizes how to steer (via countersteering) from their bicycle experience.