How the hell does counter-steering work on a motorcycle?
Ok I think you mean how one tries to "steer out of a slide" ?
Here is the deal. , the direction of the slide minus the friction of the road and tire is the BIGGEST force in one direction.
If you turn the front wheel in the OTHER direction, it helps balance out the forces and you go "straighter".
If you mean going around a turn , that is different.
What makes anything stay going around a turn is CENTRIPETAL force ( inward pulling).
That is why a banked turn is easier to go around at a higher speed.
When you lean into a turn you are putting more wt or force to the center as you turn.