The aerofoil will always pitch about the Aerodynamic center, and it depends where the average forces of the top surface are acting through, compared to where the average forces of the bottom surfaces are acting through.
With a symmetrical aerofoil the forces of the top and bottom surfaces act through the same position, so it has no pitching moment.
A cambered aerofoil will have the top surface forces acting through a point further back along the chord than the bottom forces, so it will pitch nose down.