Human and equine balance, in more than one way, do not compare.
The upright human body rests on two balancing points, one in the center of each foot while walking, and one in each seat bone while sitting. From the pelvis the vertebra rises; at its highest point balances the head. Shoulders and collar bones connect arms and hands to the neck. In stand-still the human body in essence forms a cross, which is subject to one gravitational plumb line. In the human body core and gravitation thus follow the same vector line. Skeleton, muscles, organs and all other vital systems are embedded in a strong, delicate fascia skeleton, which facilitates dynamic balance.
The horse's vertical body knows no such one single plumb line. While grazing the majority of its weight rests on the forehand. In mobilization the horse's neck rises and weight shifts to the hindquarters. In steady movement weight is distributed evenly on all four legs. In each state the body's balance point shifts to a different place. The horse's organs rest in a fascia skeleton, which hangs from a cantilevered backbone and an S-shaped neck vertebra. Unique functions in neck, upper line and hindquarters permit the horse to deal with the gravitational pull on its body, shift balance and manage locomotion.
Clearly human vertical and the horse's horizontal balance are of a different nature. The following example may further illustrate this. Human stand-still is easily defined as the absence of movement in the presence of balance. The horse accordant to its dual nature knows two types of stand-still. One is the absence of movement while resting. In this static balance four legs like columns hold up the body's mass. The mounted horse's stand-still, however, is not rest but stand-by. It requires not static but dynamic balance.
This example may serve as an introduction to SomE equitation. The horse is in command of its paces from birth. It gains experience in commanding its dynamic balance in the rider's presence, while merging its will to his.