How complex can it be? If you have a bare minimum background in basic physics and control theory, and a bicycle in your hands, the qualitative reasons for balance and stability will jump at you in under 10 minutes...
If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.
I was clearly wrong in that many people disagreed and found this to be an interesting and nontrivial subject.
Bend left -> torque to the right, bend right -> torque to the left. Here you have the basic ingredient for stability: the one torqueless angle is the bike going straight perfectly vertical wrt the ground, while any perturbation leads to a torque in the opposite direction.
I felt it was basic stuff maybe it's not?