Why a wing does not work the way the diagram shows
The equal-transit-time explanation is wrong, and what actually deflects the air.
A wing does not lift an aircraft because the air flowing over its curved top has to rush ahead to meet the air going underneath at the trailing edge: it lifts because the wing tips the air passing it downward, and the reaction to throwing that air down pushes the wing up.
I first met the usual explanation in Macaulay's The Way Things Work, a book that gets through a hundred machines using only cutaway drawings and plain description, with barely an equation in it. Its page on flight showed the familiar wing shape, flatter on the bottom and curved on top, with two arrows racing along each surface to meet at the trailing edge at the same instant. The drawing left me more puzzled about lift than I had been before opening the book, and that puzzle is what sent me looking properly into what a wing does.
The physics of a lifting wing
The standard classroom account, often called equal transit time, says that because the top of a wing is more curved than the bottom, air travelling over the top has further to go, so it must speed up to arrive at the trailing edge at the same moment as the air going underneath. Faster air means lower pressure, by Bernoulli's principle, and the pressure difference between top and bottom is what lifts the wing.
The trouble is that nothing forces the two streams of air to arrive together, and smoke-trail photography shows they do not. The air passing over the top of a working wing reaches the trailing edge well ahead of the air passing underneath. The premise the whole explanation rests on is false, so the conclusion cannot be trusted even where it happens to point in the right direction.
What is actually going on starts with the wing's angle, not its curve. A wing is set very slightly nose up into the oncoming air, and both its curved top and its flatter bottom bend that air as it passes, so that the air leaving the trailing edge is angled downward compared with how it arrived. Turning a large mass of air downward, continuously, second after second, needs a downward push from the wing on the air. By Newton's third law, the air pushes back up on the wing exactly as hard. That reaction is lift.
Bernoulli's principle still belongs in the story, correctly applied. The curved, deflected flow really does produce a lower pressure above the wing and a higher pressure below it, and Bernoulli's principle describes that pressure difference accurately. What is wrong is the reasoning used to get there, not the physics of pressure and speed itself. The pressure difference is a consequence of the wing deflecting the air, not the cause of it.
Where you have already felt this
The clearest way to feel the real mechanism is to hold a flat hand out of the window of a moving car, angled slightly so the leading edge is a little higher than the trailing edge. The hand tries to rise, because the tilted surface is shoving the air beneath it downward and slightly forward, and the air shoves back, up and slightly backward, against the hand. Nothing about the hand's shape matters much here, since a flat hand has no curved top at all, which is itself evidence that curvature is not the essential ingredient. Tilting the hand the other way makes it dive, for the same reason in reverse. A wing does the same thing at a much larger scale and with a shape refined to do it efficiently, but the underlying trick, tilting a surface into an airflow so it throws air one way and gets pushed the other, is exactly what the hand demonstrates.
The one number worth remembering
The pressure difference a cruising wing actually needs is startlingly small. Comparing the air just below the wing to the air just above it in level flight, the difference is typically only a few percent of ordinary atmospheric pressure, about what changes climbing a couple of storeys in a building. Spread over the dozens of square metres of wing on an airliner, that whisper-thin difference in pressure adds up to a force of hundreds of tonnes. Lift does not need a dramatic pressure difference to work with, it needs a large enough area and a large enough amount of air being deflected, and it gets both.
What follows from this
Because lift comes from deflecting air rather than from the wing's curvature alone, a flat board tilted at the right angle will fly, badly but genuinely, and a symmetrical wing with no curve on either surface flies perfectly well provided it is tilted into the airflow. Curvature helps efficiency and lets a wing produce some lift even at a small angle, but it is not the mechanism. It also follows that lift depends on speed and angle together rather than on shape alone, which is why the same wing produces different amounts of lift at different speeds and angles, and why pushing that angle too far eventually breaks the flow away from the wing altogether.