Unless thrown from height, the target must rise before it starts to fall!!! So your statement that “the target is always falling” is faulse and nonsense. When a shallow angle target is in the transition from riseing-falling, shooting perceived ‘at it’ will break it. An incoming crow at its apex needs to be shot ‘at’, before/after the apex is different.
In my mind, there are two different meanings of shooting ‘at’ a clay. There’s the dead gun, rifling a crow at its apex, where the gun isn’t moving as you fire and you shoot ‘at’ the clay. The other is when you are shooting swing through, you start behind a clay needing very little lead, a mini slowing down for instance or a very slow driven, you start behind, swing through the clay moving slightly faster than the clay, and pull the trigger when the sight picture is of shooting ‘at’ the clay, with the gun still moving. Telling someone who shoots maintained lead to shoot ‘at’ that type of clay will in all probability result in a miss as there Gun is moving at the same speed as the clay
p.s. “every target you shoot does the same”
tell me how every rabbit clay is dropping....