From what I read on the books, I understand that the Lift of an airfoil can be thought of as the sum of the upper Lift and lower Lift.
In symmetrical airfoils, both upper and lower Lift always act at the same point of the chord and this point, the CP, is always the same regardles of angle of attack, and happens to be at the AC.
In cambered airfoils, these lifts act at different points, so that we have a pair of parallel forces, the resultant of which acts at the CP. The CP location changes with AoA.
The existence of this pair of parallel forces reveals an effect that has an aerodynamic origin. Which exists per se. It is not the moment of any force about any arbitrarily chosen point, but a very phisical twisting torque that can be measured in the wind tunnel and expressed in Newtons-meters or whatever unit.
It is this twisting torque that I am interested in. I don't accept that we consider Lift as acting at the AC because that greatly simplifies calculations. Lift acts at the CP. That's where it acts.
I believed that this twisting moment (pitch down in typical airfoils) was decreasing with AoA, which of course meant a negative effect on airplane's stability. However, when taking the AC as the origin of moments and deriving in the stability equation, this effect is "magically" eliminated, and I can't understand why they do that. I just don't buy it.
I accept empirical evidence, but I don't like when mathematical tricks are used. Then I get lost not because of my mathematical ability (I was very good at that years ago) but because they (not you, the books) are cheating.
I know well what the CP is and what the AC is. But I think the aerodynamic pitching moment is unduly simplified by everybody.