The old Bernoulli explanation of how planes fly. As Jef Raskin liked to point out, if this were the case then an upside airplane would accelerate to the ground (just like an upside down VTOL aircraft does) but instead it can fly by just adjusting its angle of attack.
There is indeed a difference in pressure on top and on the bottom of a wing but the main function of the wing is to accelerate the air it passes through towards the ground (like a ceiling fan's blade does). The air goes down, the plane goes up just like Newton intended. The block of air going down is only as wide as the wing - the air to the left and to the right of the wing is not affected. At the transition you are adding a rotation, hence the wingtip vortices.
Any kid who stuck his hand out the window of their moms car and played with the angle of attack knew that the whole airfoil explanation of lift was hogwash. Stick any flat thing out the window and tip it up or down and you instantly feel a corresponding force.
There is indeed a difference in pressure on top and on the bottom of a wing but the main function of the wing is to accelerate the air it passes through towards the ground (like a ceiling fan's blade does). The air goes down, the plane goes up just like Newton intended. The block of air going down is only as wide as the wing - the air to the left and to the right of the wing is not affected. At the transition you are adding a rotation, hence the wingtip vortices.