For example, yes, the air above the wing moves faster than the air below the wing, and it's related to shape of the airfoil.
However, it has nothing to do with magical "air has longer to travel".
It starts with how combining flows at the trailing edge of the airflow create a vortex which induces an opposite vortex around the wing, which is a bit counter-intuitive (but it has nothing on why swept wings work, which can be summarised for practical aircraft design purposes of "because if we calculate at an angle we get better values and reality is crying in the corner")