Muck out a plenty stables everyday, come home smelling like pony and dirty as hell. Maybe you'll convince them based on work ethic. If that doesn't work then they might relent If you agree to come home with less gunk on your noggin 😁/in your hair/on your toesh.
I would include the benefits of growing as a person: responsibility, confidence etc. also would say how you will meet new lifelong friends. The experience will help you create an opportunity for future jobs as well. @ana S
You could say you're a competitive person and you could have the chance to make new memories and meet new people to make your equestrian community larger for support, friends, etc. also, it could be a good way to see how you are improving and what needs to be worked on. (Mostly make it sound extremely beneficial towards you and your riding, yknow?) mkay hope that helped! Good luck