Why don't the wings of a airplane have to flap like the wings of birds?

The wing is made flat on the bottom and curved on the top. The air underneath has a shorter distance to go to get to the end of the wing, that is straight so. The air over the top has further to go because of the curve so the air travels faster. This causes 'low preasure' above the wing. This makes the air around the wing rush in and 'sucks' the wing up causeing lift.

The exact same thing happens on a bird wing except they do not have engines to push them forward. So the bird flaps its wing to push the air behind them and down which gives them lift and pushes them through the air.