It only needs to be slightly more determined to be leader than the leader is to remain leader. When people understand and are able to use herd dynamics AND are determined to be leader, the balance can be maintained - mostly because the human has better reasoning capabilities than the horse. To the leader it really makes no difference what the choice is because the leader is convinced it can win the fight and really won't lose any sleep if the rebel leaves. But it does matter to the rebel. If the rebel has ANY doubt whatsoever it can best the leader it will not try to best the leader.
Survival is in being part of the herd.
In the herd it has many more ears and eyes and it only needs to run faster than the slowest member when a predator approaches. If it leaves, it must find another herd as soon as possible. Unable to do that it then seeks to rejoin the herd it was banished from. Soon the rebel is not a rebel anymore. Since the horse is pre-programmed to react to the actions of the leader the fact the actions are being performed by a human has no bearing.