Not to say they can't be useful tools but they fall into the same basic traps and issues despite our continues attempts to improve them.
https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...
The "wrong" answers all have a bit of truth to them, but aren't the whole picture. As with many complex mathematical models, it is difficult to convert the math into English and maintain precisely the correct meaning.
Exactly. The comments in this subthread are turning imprecision in language into all-or-nothing judgments of correctness. (Meanwhile, 80% of the comments advance their own incorrect/imprecise explanations of the same thing...)
It gets complex if you want to fully model things and make it fly as efficiently as possible, but that isn't really in the scope of the question.
Planes go up because they push air down. Simple as that.
You wouldn't explain how swimming works with pressure differentials. You'd just say "you push water backwards and that makes you go fowards". If you start talking about pressure differentials... maybe you're technically correct, but it's a confusing and unnecessarily complex explanation that doesn't give the correct intuitive idea of what is happening.
Air molecules travel in all directions, not just down, so with a pressure differential that means the air molecules below the wing are applying a significant force upward, no longer balanced by the equal pressure usually on the top of the wing. Thus, lift through boyancy. Your question is now about the same as "why does wood float in water"?
The "throwing something down" here comes from the air molecules below the wing hitting the wing upward, then bouncing down.
All the energy to do this comes from the plane's forward momentum, consumed by drag and transformed by the complex fluid dynamics of the air.
Any non-zero angle of attack also pushes air down, of course. And the shape of the wing with the "stickiness" of the air means some more air can be thrown down by the shape of the wing's top edge.
It is not that simple.
The point is that a flat plane with full flow separations is the minimum necessary physics to explain lift. It would obviously make a terrible wing, and it doesn't explain everything about how real wings are optimised. That's not the point.
In any case, I only said the wing pushes the air down. I didn't say it only uses its bottom surface to push the air down.