3 ideas
What a horse does under force it does without understanding and without grace, like a dancer made to perform under the whip. Only behavior the animal performs willingly, drawn out through reward and ease, becomes both reliable and beautiful. So a trainer should create the conditions in which the desired action is the horse's own choice rather than extract it through pain.
When the horse does what is asked, the rider should instantly give it ease, such as a slackened rein or a rest, so the horse links the action to relief. When it errs, the rider should correct it calmly, because anger makes a rider act rashly and do things they later regret. The timing of relief and the absence of rage together form the teaching signal.
A horse that shies at an object is usually afraid, not stubborn, and punishing it confirms that the object is dangerous. Seeing resistance as fear rather than disobedience changes the fix from punishment to gradual, supported exposure.