Why Horses?

I have often thought why the use of horses in battle.  Many times in battle a person would ride into battle wearing chainmail also dressing their horse up in chainmail .  The reason I wonder why Horses were used is because there are many large animals that could just as easily be made tame, and dressed in chainmail to ride into battle, many of which more sturdy, and resiliant than the horse.  It is my belief that the horse was used though, because of it's natural fight or flight reaction to which the horse will actually run towards its persecution rather than from to scare, or threaten those apposing it.  So therefore it leads me to believe that even though any chainmail covered animal would be threatening and rather combersome to a battle, the horse is used due to it's naturalness to the idea of running towards battle rather than from it, the courage of horses has lead many people into battle bringing enemies to their knee's.