This myth -- that the Bernoulli effect is what causes lift -- is so pervasive that even most pilots and geeky engineer types believe it. What actually happens is that the airfoil moves through the air at a slightly nose-up angle causing the air to be directed slightly downwards as it flows by. An "equal and opposite reaction" to the downward flow then occurs in the form of a lifting force. So it's actually an airflow vectoring effect, not Bernoulli, that lifts a plane.
The classical demonstration of the Bernoulli effect is to blow air over a strip of paper and watch as it rises, but actually this disproves the Bernoulli effect and proves the vectoring effect instead! If Bernoulli were the operative mechanism the strip would continue to rise and curl towards your face. But what actually happens is the strip rises till it's almost level and then rises no further. This is because the laminar flow is no longer directed downward, as it was when the paper was drooping, but rather outward and therefore not creating any lift.
That lift is caused by airflow vectoring is why symmetrical airfoils can work. It's also why the Wright brothers wing worked. Their airfoil seen in cross section was a curved line, not a volume-containing curve, so the air above and below the wing travelled the same distance. Since the Bernoulli effect requires the upper and lower flow to travel different distances (and therefore at different speeds), Bernoulli couldn't be what lifted the Wright brothers' aircraft. It actually was vectoring, just as it is on modern aircraft.
Pretty crazy, huh?