The precision of figures is a hallmark of dressage, not just because dressage riders are a neurotic crowd, but because accuracy helps your horse build muscles symmetrically and helps him move fluidly. Accuracy helps him stay straight so all his energy goes in the same direction—toward the bit.
If you look at the lines in a standard arena, it’s the rider’s job to keep her horse on one of those lines. If you’re not on one of those lines, ride another one that is clear, defined and determined by you. If you aren’t determining the line of travel, your horse is. And if he’s determining the line of travel, he won’t be doing it in a gymnastic way. It’s your horse’s natural inclination to move in a way that is as easy as possible—which isn’t the way of the ballerina or the gymnast. If he’s determining the line of travel, he will lose his straightness and his balance.