Bernoulli's principle is indeed how airplanes fly. Your link shoots down the silly equal-time theory, not Bernoulli's principle.

Basically, airplanes fly for three reasons:

1. The wing deflects air downwards. 2. Air moves faster over the top of the wing than over the bottom. Much faster than the equal-transit theory indicates. 3. Air pressure is higher on the bottom of the wing than on the top.

The important thing that few people seem to grasp is that all three are equivalent statements. They aren't additive. There aren't three different reasons airplanes fly, there's one reason airplanes fly, with three different ways to look at it.

This interesting. You say there is one reason airplanes fly. But "deflecting air downwards" is causing an lifting force by action=reaction (the way a rocket works) and "air pressure is higher on bottom of the wing than on the top" is causing a lifting force by pressure differences.

Those are different reasons, or am I mistaken here?

Nope, they're completely inseparable. If you deflect air downwards, no matter how you do it, you must end up creating a pressure differential where air pressure is higher on the bottom than on the top. If you create such a pressure differential, then no matter how you do it, you'll end up deflecting air downwards.

Pressure is just a fancy way of saying force per area. The air pressure on the bottom of the wing is just the downward force exerted by the wing on the air, divided by the wing's area. The only way to deflect air is by applying a force to it, and the only thing applying a force to it is the wing.