Why is a three legged stool not rock as much as a four legged stool?

Three points are the minimum required to define a geometric Plane. Any 3-legged stool, then, can only exist on a single Plane, and cannot alternate between any two Planes (i.e., rock).

By combining any 3 of the 4 or more legs on the stool could define a separate plane on which the stool could stand. There are 4 separate configurations of 3 legs upon which a 4-legged table could stand:

ABC

AB D

A CD

BCD