What is a "dressage"? Submission of a horse to the man or discovery and development of its natural abilities and possibilities?
Probably, both are true. And different duets “man-horse” incorporate those components at different ratio. But nobody sees and values a kitchen! Everyone is not interested in process but result. And result is a mystery of springy motions, smooth calligraphy of lines, noble mutual attentiveness, a wonderful unity of the man and the horse and entire submission Strength to Beauty. Probably, we like “training” for that.