You can test this out yourself with a pencil or a ruler...
By supporting a rod from two points with your hands, a normal force is produced at each hand.
The hand which is supporting more of the weight of the rod will have a greater normal force, and therefore be able to withstand more static friction before sliding.
As a result the hand farthest from the rod will always slide toward the center of gravity of the rod, while the other hand remains static against the rod.
The end result is that your hands will always come together at the balance point of the rod.
Furthermore it does not matter if you add additional mass to one side of the rod and shift the balance point, there the hand supporting less weight will always be the hand to slide against the rod, and your hands will still come together at the balance point of the rod.