"See how it flies" that you linked is a wonderful resource for understanding the physics of aircraft and the skills needed to fly one.
Another, more math heavy treatment, of why airplanes fly that still aims to gain a conceptual understanding is "Understanding Aerodynamics" by Doug McLean: https://www.amazon.com/gp/product/B00B9QLBH0
I have that book! I bought it some time ago; I don't remember why I bought exactly that book, I guess it was recommended somewhere online much like you did just now.
Unfortunately I haven't found the time/energy to start reading it.
Another, more math heavy treatment, of why airplanes fly that still aims to gain a conceptual understanding is "Understanding Aerodynamics" by Doug McLean: https://www.amazon.com/gp/product/B00B9QLBH0