This is counter-steering. Because we have learned that steering a motorcycle is an effortless chore. It feels like that because the harder we push it, the more the motorcycle turns to the right and, thus, it feels like the right grip is pushing back at you that much harder. In other words, we quickly learn to associate counter-steering feedback with the hand closest to the direction in which we wish to turn. Further, even a little bit of experience shows that counter-steering is essentially effortless while trying to turn the handlebar in the direction you want to go is virtually impossible .
Humans are relatively fast studies, after all.
The phenomenon is called Gyroscopic Precession . This is what happens when a lateral force is applied to the axis of a spinning gyroscope. The spinning gyroscope translates the force vector ninety degrees off the direction of spin. Thus, if we try to turn our front wheel to the left, the force we use appears as a lateral force forward against the axle on the right side and this is translated into a force that tries to lean the wheel to the right. Similarly, trying to turn the wheel to the right results in the wheel trying to lean to the left.