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From what I read, an airplane's wing always has a forward-pitching moment which is a torque that tends to rotate the plane nose down. Is this moment nonzero for any angle of attack (zero, positive, negative)?

A torque needs a force and a distance (lever arm). I think the force in the pitching moment is the lift force ##L## and the lever arm ##d## is the distance from the lift to some specified point, for example he center of gravity ##CG##. The force ##L##, applied at the center of pressure CP, varies in strength and position with changes of the angle of attack. For stability, in case of wind gusts, the center of gravity ##CG## of the plane is placed ahead of the CP. Thanks to the horizontal stabilizer in the back, an aerodynamic downward force is generated that keeps the plane stable. By itself, the wing would be highly unstable. So there are two torques: the CCW torque due to ##L## about the ##G## and the CW torque due to the stabilizer force about the ##CG##. The force of gravity produces no torque about its own position.

My question: why is there this natural forward pitching moment in the airfoil? Why aren't planes designed so the ##CP## and the ##CG## are in the same spot? If ##CP## and ##CG## were at the same point, we would not need the rear horizontal stabilizer...

Thanks!