It is said that wing alone is unstable, because it provides a nose up moment, so tailplane is needed to damp it. But normally wing provides a pitch down moment (as far as I know, apart from very high aoa situation) because centre of pressure is behind the centre of gravity. So shouldn’t wing moment be actually stabilising? I’m confused about stability, because we one time we consider stationar lift acting in aerodynamic centre and moving centre of gravity, next time moving centre of pressure with stationary centre of gravity and so on... please help me out.
It's not about the moment but its change with AoA.
Any wing can be trimmed when the cg is at the center of pressure. What counts is how things change when AoA changes.
If you want stable behavior, use an inverted airfoil. A regular, cambered airfoil will cause unstable behavior.
For a trimmed airplane the moment around the center of gravity is zero. Now it is important how this moment changes when the airplane moves away from this trim point. If AoA increases and the moment becomes negative (nose down), the airplane is stable.
If the center of gravity is too much forward, the airplane cannot be trimmed in the first place because control authority is insufficient to produce enough downforce at the tail in order to compensate for the pitch-down moment of the lift force on the wing around the more forward center of gravity.
But normally wing provides a pitch down moment (as far as I know, apart from very high aoa situation) because centre of pressure is behind the centre of gravity.
If we are using the archaic "Center of Pressure" concept-- as opposed to the newer concept of an "Aerodynamic Center" combined with a "pitching moment"-- then we can observe that the Center of Pressure of the wing moves forward as aircraft pitches up (increases angle-of-attack), and moves aft as the aircraft pitches down (decreases angle-of-attack). This is clearly destabilizing.
Assuming we are speaking of an aircraft flying in a trimmed condition, your observation that the center of the pressure of the wing is behind the Center of Gravity of the aircraft is in fact true, if the horizontal tail is creating a downforce. But this does not imply that the aircraft would still be stable if we removed the horizontal tail.
It appears that you may be making the mistake of assuming that the wing's Center of Pressure is operating at a fixed location behind the CG of the aircraft, regardless of changes in angle-of-attack. If that were true, that would imply that the aircraft would tend to pitch down to a lower angle-of-attack whenever the airspeed increased, and would tend to pitch up to a higher angle-of-attack whenever the airspeed decreased. That wouldn't be a stable situation either.
I'm going to try a mental analogy exercise that I hope the experts on here will accept. Leaving out many of the complex moments and forces at play, just for the purposes of conceptualization by the layperson or semi-layperson. See if it works.
It's important to separate stability and trim.
Static stability in pitch, in very crude terms, is really just a "vertical weathervane effect".
Take an airplane, locate its center of mass, and turn it sideways and stick it on a spike on a tall pole, with the spike on its center of mass and the sideways airplane free to pivot on it, nicely balanced on the spike. As long as the aerodynamic center of the entire body, fuselage, wings, and tail, the point where aerodynamic forces acting on all those surfaces is focused (the Neutral Point), is aft of the spike, the airplane will point into wind, like a weathervane. And if the wind shifts, it will move to point into the new wind direction. It's positively stable in its weathvane-pointing.
Move the spike back so that it's coincident with the Neutral Point, and it will no longer weathervane and will just want to point any which way independent of the wind. It's weathervaning stability is neutral. Move the spike farther aft to behind the Neutral Point, and my weathervane plane will want to switch ends - its weathervaning stability is negative.
In other words, the Neutral Point wants to trail the C of G if there is any offset between them, and if it's right on the C of G, it doesn't want to do anything and the body is free to drift aimlessly. Positive static stability requires the Neutral Point to seek to trail the C of G in the correct orientation.
Turn the whole thing back level again, and the same thing is happening except that the wind's changes in orientation is vertical instead of horizontal, and we call it Angle of Attack. When the change occurs, the airplane, being a free body, rotates about the CG (where the spike was) to keep its orientation into wind, to maintain a certain Angle of Attack, as long as the Neutral Point of the plane is aft of the C of G. The Neutral Point wants to trail the C of G, in the vertical plane, and the airplane is positively stable.
Trim is process of creating a variable balance of forces between the fore and aft lifting surfaces that allows the "pointing angle" of the overall body to be adjusted relative to the air stream.
Going back to the vertical plane-on-a-spike, if the wing and tail surfaces are all aligned, the whole thing will point into wind straight, with no angle off the wind. If I change the incidence of the tail surface to generate a lateral force, it'll rotate the plane out of wind until an opposing force from the front surface, the wing, applies a moment that cancels out the one from the rear surface. My sideways airplane weathervane will now orient itself with into wind with some offset, say 5 degrees off the wind, and will rotate when the wind changes to point with that 5 degree offset. This is because, when the wind changes, the balance of forces between the main and aft surfaces that created the 5 degree offset is skewed, one force is stronger than the other, and it seeks to rotate to restore the force balance, which occurs with the 5 degree offset.
Turn it back horizontal and it's the same, except that the offset wind pointing is now a vertical orientation, Angle of Attack. When the tail surface's incidence is moved to position X, an imbalance of forces is created relative to the wing, and the plane pitches, about the C of G, until the pitching forces of the wing opposing the forces of the tail are back in balance, and the plane flies with an offset to the airstream, an Angle of Attack. Being able create any required stability point Angle of Attack allows us to make the wing make lift that supports everything without having to have it on a horizontal pole with a spike on it to hold it up.
If I set the horizontal tail to achieve a balance of forces with the wing at a 5 degree offset, the body will rotate in the vertical axis to maintain that 5 degree offset, or Angle of Attack. If I change the incidence of the tail to create more force, the equilibrium point is changed, say to 10 degrees, and the plane will point in the vertical plane, to maintain the equilibrium point that is now found at 10 degrees. And because the Neutral Point is in it's correct location aft of the C of G, it will positively seek to regain that 10 degree Angle of Attack if the vertical wind orientation changes.
We have positive static stability at our trim Angle of Attack (to the pilot, trim speed, since speed and AOA are directly connected), and if I move the stabilizer surface to another position, our stability will be relative to a new Angle of Attack (and speed), and the plane will actively seek to achieve and maintain that new Angle of Attack thanks to the Neutral Point's offset from the C of G.