Question

Why does lowering the center of gravity increase stability? What is the exception?

Answer 1

Lower the CG means lower potential energy of the system and hence more stability.

We know in nature, everybody tries to attain a state of minimum energy. For example when you jump from a height why do you come down? Because when you are at a height you have a higher energy associated with you, so when you jump nature tries to bring you down to the state of minimum energy, which is in this case the ground. Hence, lower CG means greater stability.

The only exception that I can think of is: Suppose you are standing vertically but your legs are bent in a slanted V position.

So even though the CG is low, the line of gravity is close to the base edge. Hence, very small force could displace it outside of the support base.