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It's easiest to understand as a black box, or a "control volume". Consider the air coming in the front (horizontal) and the air going out the back (velocity is deflected downwards). Momentum change, needs a force to keep things in balance. Simple! Fluid mechanics is all about that kind of thinking.

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This is exactly one of the common pathways through that middle section, which is nice and simple but doesn't really explain anything (why is the air deflected downards?).

Because the plane has speed and trading that speed for lift

OK, but that's just saying "the aerodynamic force exists, because we can observe the plane goes up and the air goes down", isn't it?

Classic phenomenological analysis. "This is not reality, but as a model it's good enough for a first pass design analysis"

It's control volumes all the way down. Look up "Finite Volume Method" in CFD.

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