Center of Gravity and Center of Lift stability
If you ever read something along the line that &quot;even the slightest&quot; cause will result in &quot;very bad changes&quot; when before all was stable, you know that the writer was out of their depth. But you have come to the right place.
The way you formulate the question it concerns lateral stability. The combined center of all side forces (= lateral lift) should be behind the combined center of gravity of all components of the airplane to give it weathervane stability. Since the law of conservation of momentum applies also to a flying airplane, all movements should happen around its center of gravity, so all moments should be summed up there to see what effect they will have. In order to see their effect on stability, it is even better to focus on the force changes effected by a change in sideslip. If they produce a moment which will rotate the airplane away from that sideslip, the airplane is laterally stable.
Why only the changes in sideforce with sideslip? This will become more clear when we look at longitudinal stability, which is implied by the graphic in your question. Here the same principles apply, only that a constant downward acceleration is added, namely gravity. To compensate its weight, the airplane needs to produce an opposite force, namely lift. This lift has to act at the same longitudinal and lateral position of the center of gravity. Any deviation would produce a moment around that center of gravity which would start a rotation. In order to shift the center of lift to the desired location, the pilot will deflect control surfaces to modulate the lift force at the extreme ends of the airplane (tail rsp. canard and wingtips) so that any moment around the center of gravity disappears. This is one meaning of &quot;trimming&quot; the airplane (the other one means to remove all stick forces in order to stay at this state).
Theoretically, the pilot could balance the airplane in the desired state using the control surfaces like you can balance a broom on your fingertip. But that becomes tiring quickly. So it is preferable that the airplane itself will produce moments when the trimmed position is left, without any additional control deflections. This is achieved by having the changes in lift force act at a location behind the center of gravity.
The point where all lift forces can be summed up is the center of pressure, (Auftriebsmittelpunkt) whereas the point where all changes can be summed up is the neutral point (Neutralpunkt). Now you know what the author of the Wikipedia article wanted to say but failed to do so. He is by far not the only person to confuse those two points.
In fact, only when the center of lift coincides with the center of gravity will flight be straight and steady. All other positions will cause the airplane to rotate away from its current attitude. In order to return to its old state, only the neutral point needs to behind the center of gravity.