The takeaway is that the correct explanation involves too much math, like complex analysis. If someone want to skip the math and use hand waving, the explanation is allays oversimplified and usually wrong. [I tried to find a link to a small easy to understand and correct explanation, but I couldn't.]
There really isn't much intermediate space between "An airfoil disturbs the air in such a way that the pressure on top is lower than the pressure on the bottom" and potential flow calculations...
Note that potential flow calculations are significantly oversimplified; they work only for thin airfoils at low angles of attack (so they will correctly model basic flight, but not anything beyond that)[1].
So lets say you get an intuition of flow separation and turbulance on a 2D cross-section (which is already a bit of a stretch) you now still can't explain how a delta wing works.
Really smart people who know a lot about how flight works and have expensive computers still need to test their ideas in wind tunnels.
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