Why should the centre of mass be ahead of the centre of pressure?
On most airplanes, the horizontal stabilizer provides a downward lift. The center of mass is between the nose gear and the main gears.



If the center of mass is too aft:


Stall (and spin) recovery will be difficult or even impossible
Increases the chance of tail strike
The plane will tip on its tail if the main gears are not moved aft


If center of mass is aft of center of pressure, then the horizontal stabilizer must provide positive (upward) lift; the tail structure must be made stronger to support the higher lift. The wings will be moved forward of the main gears to keep the aircraft balanced on the ground. Such designs are called Tandem wing. See also this question.