Here is a simple analogy to understand the center of gravity and it's relationship with the center of pressure. Think of an archers arrow, when it is shot from the bow, what makes it keep the pointy end forward? In short, it is the relationship of CG to CP.
Remove the fletching and examine the arrow in your mind, assume that there is no heavy weighted tip and the entire arrow weighs the same from tip to tip. The center of gravity would be the middle of the arrow since the entire structure has the same mass. If you were to shoot that arrow, it would not keep the pointy end forward because the arrow would want to rotate around the center of gravity. The aero forces running around the shaft would make it wiggle and wobble, but it would not fly straight.
Now, take the arrow and put a pointy heavy tip on it. Now, shoot it and imagine what it does. The added mass to the front of the arrow moves the center of gravity forward. This will make the arrow TEND to want to stay pointy end first, but it will not fly true.
Add the fletching back on and viola, it wants to fly true. The fletching provides stability by moving the center of pressure to the rear of the center of gravity. By holding the relationship of CG forward of CP, you gain stability. The reason some cars want to swap ends is that the CP is too far forward, or in front of the CG. If a car that had tendancies to swap ends had some modifications to move the CP aft, it would prevent them from spinning, it would also move you out of several classes and increase the drag on the vehicle.
Wait for the roadster guys to chime in, they have classic examples of swapping, spinning and some tricks to minimize its occurrence.