I've held off long enough. There is one piece of the discussion that is missing, and it is critical to understanding the nose heavy stability vs. the tail heavy instability. That is the relationship between the center of gravity and the center of lift.

The center of gravity is the point at which all the downward forces due to gravity of the plane appear to act. Commonly referred to as the center of balance or the balance point. That is the center of the balanced teeter-totter.

The center of lift is the point at which all the upward forces generated by the aerodynamic forces on the plane appear to act. In the case of the teeter-totter, it is the fulcrum of the lever.

When the center of lift and the center of gravity perfectly coincide, there is no differential force generated between the two (that is rotational force on the airplane). The airplane will move in the direction it is pointed without input.

This condition has no tendency to correct the planes attitude, thus it has no dynamic stability, but it is not unstable. A plane flys with no up elevator trim, and inverted flight requires no elevator input (assuming a symmetrical wing). For an asymmetrical wing (typical air foil), the center of lift changes when inverted, so different discussion.

When the center of gravity is forward of the center of lift, that generates a force that tends to want to drop the nose, that is nose heavy. This condition is normaly corrected by adding some up elevator. Consequently, when a plane with a symetrical airfoil goes inverted, we need to input down elevator to prevent the nose from dropping.

The nose heavy condition has another benefit, that is dynamic stability. As the direction of the wind over the wing changes (turbulence), the wing will generate a rotational force that points the wind into the changed wind direction. Thus the plane will continue to fly with the wing pointed into the wind over the wing. Since the air is normally flowing front to back over the wing, the flight of the plane is stable.

Now the tail heavy condition. When the wind over the wing changes, the rotational force that develops between the center of lift and the center of gravity tends to cause the wing to rotate opposite the desired direction. This happens with any change (such as small elevator movements). The plane is dynamically unstable, because it reacts to worsen the condition. Somone earlier had used the analogy of the dart, but it got edited out, but it was exactly correct. This dynamic instability can be overcome to a small degree by the elevator and pilot, but it doesn't take very long before the plane becomes uncontrollable, and any control input becomes grossly exaggerated. NASA used to have an animation on the web that showed this effect.

I know this is a long explanation, but its not a simple effect.

Brad