Why 1/12 use negative caster gain?

reduces caster at turn in and increases it at exit

As you turn the wheels during cornering the angle of the caster affects the angle of the camber. The more caster you run the more the outside wheels camber will be increased negatively as the wheels turn. Since this camber increases the more you turn the wheels, called dynamic caster instead of static caster.

let say, 2 caster 2 -ve camber,0 reactive caster, when cornering, outside wheel  will change to 3-4 -ve camber, result in reducing the contact patch area traction
Using a reactive caster can reduce the excess camber and control  the contact patch size .