Dutch roll
The vertical tail provides the damping for dutch roll (that is why we put the yaw damper on the vertical tail to eliminate the DR). The longer the "arm" is to vertical tail from the cg, the more effective it will be. Hence, if the cg is forward, the moment arm to the vertical tail is the greatest providing the largest restoring moment.
In addition, the "fueslage tube" that is forward of the cg is destabilizing (e.g. doesn't help the aircraft turn back into the wind) whereas that part of the fuselage that is aft of the cg is stabilizing. Thus, moving the cg forward allows more of the fuselage to contribute to overall stability.
This being said, as the aircraft is yawing, the amount of wing sweep and dihedral in the wing will greatly affect the phi to beta ratio (e.g. the amount of rolling versus yawing motion encountered) and the overall behavior of the DR as well.