The aerodynamic lift on the wing of an airplane (airfoil) is generally explained by the argument that the faster speed of the air along the top of the wing leads to reduced air pressure there and hence produces a lift (Bernoulli's Law). Using this argument, one should also expect a lift for a symmetric wing profile as shown in Fig.1.
Symmetric wing profile Fig.1
However, if one considers the problem from a microscopic point of view, one comes to a different conclusion: upward and downward forces should exactly cancel for a symmetric wing profile. This is easy to see if one simplifies the situation and replaces the curved wing surface by two plane sections (Fig.2)
Schematic illustration of symmetric wing profile Fig.2
If the wing is stationary, the pressure on all parts of the wing is identical, i.e. there is no lift. If the wing is moving in the indicated direction and assuming an inviscid gas, the front half of the upper wing surface experiences an increased pressure because of the increased speed and number of air molecules hitting it (due to the orientation of the surface, this creates a downward force). On the other hand, the rear half experiences a reduced pressure because the of the reduced speed and number of air molecules hitting it (creating a lift) (for a more detailed theoretical analysis of this see the page regarding aerodynamic drag and lift). Overall, there is consequently no lift, but only an anti-clockwise torque. It is obvious that an overall lift is only achieved if the rear section of the wing has a larger area than the front section, i.e. one would get the maximum lift for the following profile (Fig.3)