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Doug McLean (Boeing Technical Fellow) has a quite decent talk about the question of intuitive explanations for aerodynamic lift: https://www.youtube.com/watch?v=QKCK4lJLQHU

Also Philippe Spalart's quote is right on the money: "It's easy to explain how a rocket works, but explaining how a wing works takes a rocket scientist".

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We have trouble explaining it at a lay level, but we can solve the entire time-varying (for unsteady cases) 3d flow field around a wing to very high accuracy. Lift seems like it should be intuitive because we've experienced the force of wind and see birds flying, but therein lies the rub. Straightforward results arise from a series of complex, interacting phenomena.

Another example might be explaining why sticky tape is sticky.

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