A more rigorous explanation of aerodynamic lift.
vuo does an excellent job of explaining why the popular theory, also called the equal transit time fallacy, is false. His explanation of lift using the Coanda effect, is partially right, but incomplete, and is not the method engineers use to calculate the distribution of forces acting on a body in a fluid flow.
First, a word on the coanda effect. The coanda effect refers to the tendedncy or a jet of fluid to follow a curved surface. This is self evident because a fluid follow streamlines, and any non-permeable surface is a streamline. And it is true that the fluid flow is derected downwards as it travels over the surface of the airfoil, and this change in momentum requires a downward force on the fluid, and an equivalent upward force acting of the airfoil, via Newton's second the third laws. The problem is that it is very difficult to use this information to get useful data on the distribution of the forces acting on the airfoil. This information is important because it describes the pitching moment created by the wing, which is important for the stability and control of the aircraft.
So how can we find that info? The answer is by using the continuity equation, and bernoulli's equation. The continuity equation relates the velocity of a fluid flow with the cross sectional area of the flow. If a fluid flow has to flow through a smaller area, it must speed up for the total mass flow to be the same, and vice-versa if the area increases. Bernoulli's equation shows that the static pressure decreases as the fluid velocity increases. When the flow hits our airfoil, it splits in two, and the top stream has to be squeezed over the top, while the lower stream has a pretty smooth and uninterrupted path. So the top stream has to speed up, and thus the pressure drops, and the pressure differential creates lift. This theory predicts that the suction will be strongest at the front of the airfoil, and gradually taper down towards the rear as the flow area increases and the flow slows down, and this is exactly what we see in wind tunnel tests of actual airfoils.
Keep in mind that the conservation of momentum isn't necesarily wrong. Do the pressure forces cause the flow direction to change, or does the changing flow direction cause the pressure forces? It doesn't matter, F=ma, the two are complimentary, so if you know one you can find the other. The change in momentum explanation is good for explaining lift to people who have a good basic physics background, but aren't well versed in fluid dynamics, but the continuity/pressure explanation is what is used by actual aerospace engineers to find the forces acting on airfoils and other bodies moving through fluids.