The purpose of being able to disconnect the front sway bar on a straight axle vehicle when off road is to allow the left and right front tires to move up and down somewhat independently. With the front sway bar connected, whenever the wheel on one side goes up the sway bar tries to also lift the other wheel. When one wheel moves up like to go over a large rock the sway bar tries to move the other wheel upward too. Likewise with sway bars disconnected, when one wheel drops, like into a hole, the sway bar tries to make the other side drop. This causes the whole vehicle to rock side to side more. With the sway bar disconnected articulation is improved because each wheel can move somewhat independently. Besides giving a much more comfortable ride off-road, having the sway bar disconnected tends to keep both front wheels on the ground and thus improves traction.
A sway bar is basically intended for highway use. In sharp turns, particularly at high speed, the sway bar tends to reduce a side to side rolling motion of the chassis particularly in turns at high speed.