What he said is not totally wrong. But since he is not given a lecture, he elliminates some of the process between.
Reducing airplane weight (m) will increase a for a given F. The velocity is a vector, the uplifting force should be related to the velocity component perpendicular to the bottom surfaces of wings and plane body. The bottom surface of the wings can be changed easily through control. But the bottom surface of the plane can be changed only by this attack angle.