The lift does not push a plane or kite forward, simply up. This is what the engine or wire is for.
Lift in a wing works by the air on the top of the wing being directed downwards at the back of the wing, such that there is a downdraft at the back. This provides the equal and opposite force of lift. The specific geometry of the wing allows for this. And you have to have the air moving across the wing with considerable speed for this effect to be significant, thus kites only work in high wind and planes need to be going very fast.
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