Well, I just graduated an AerospaceEngineer and I wanted to prove I still understood/remembered this stuff after a summer... so here for your viewing (and learning) pleasure...
An aircraft is only dynamically stable in the air (trimmed) when all its moments add to zero. Presented above are the primary contributors to your pitching moment and how they balance. I tried to give emphasis to larger forces/distances which produce larger moments. The two most important forces on an aircraft is its main wing lift and the weight of the aircraft. In a STATIC sense, these two forces must be nearly equal, therefore if your CG moves behind your neutral point you have two VERY large, nearly equal, forces trying to pitch your aircraft's nose into the air. Contrary to popular belief, the horizontal tail is actually not providing a downward force at all times. In fact (as stated earlier) in fighters, you want your horizontal tail to be as unloaded (producing little force) as possible. This is done by balancing the moments from your wing lift and CG. A loaded horizontal tail creates drag, and this is wasted energy.
One also has to realize that a neutral point is not really tied to the physical world like the CG or an aerodynamic center. A neutral point is just the point where if you move your CG beyond that point, your aircraft becomes dynamically unstable. Its kinda a question of which comes first... the neutral point or the tail design.