What I think is missing is that Cl is not a constant, but a complex curve depending on AoA. When the AoA becomes too large, Cl will reduce quickly and that means lift is lost.
The article already hints at Cl not being a constant, or at least not a constant across the whole possible range of AoAs:
For thin airfoils, at small angles of attack, the lift coefficient is approximately two times pi (3.14159) times the angle of attack expressed in radians.