Pitch moment is created by lift created by the horizontal stabilizers via the elevators.
But then main wings also create lift, why does not this lift enough to create pitch moment?
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Of course it creates a pitching moment! Now we need to define around which reference point this moment should be measured.
If the reference point is the center of gravity, it is even equally strong as the pitching moment of the elevator, it only has the opposite direction.
If you use the aerodynamic center as the reference point, the moment will be less strong. If the wing airfoil is symmetric, the moment will actually be zero (ideally), but with a cambered airfoil there is still a measurable moment left.
A moment is always a combination of a force and a lever arm, measured perpendicular to the direction of the force. Only when the lever arm is zero will the moment disappear. If we use the center of gravity as the reference point, the weight will have no lever arm and will contribute no moment, but the distance between the wing's lift and the center of gravity is large, so this moment is large, too.
Pitching moment is usually defined relative to the centre of gravity. The main wing does provide a pitching moment, since it has both a force and a moment arm relative to CG.
The reason to define pitch relative to CoG is that in a free response in vacuum, the CoG is the centre of pitch rotation. But moments can be defined relative to any point, also to the centre of lift of the main wing, which holds the aeroplane up when flying. And if we do that, we can see why the tailplane lift often points down, not up:
As mentioned in this answer this is mainly a safe configuration at low airspeeds. At higher speeds the upwards lift of the tailplane is fine and will create an aerodynamically stable configuration.