Sharing teaches responsibility. I barely thought about what I was doing with riding school horses in relation to either mine or my mount's safety. You just get told to canter at C, trot at X etc, and you don't question it in a riding school. But when you're sharing, there's no-one telling you what to do, so you learn to think for yourself. If you go out hacking, you have to find a safe place with good ground if you want to canter. You have to decide how fast and how far the horse can go safely. Sharing really has taught me so much about responsibility - I took so much for granted at riding schools.
Also, you're going to learn a lot more about stable management if you share. You're likely to learn about horse ailments, injuries and illnesses if you share, whereas at a riding school you don't really get to see that side of things.
Sharing's a much better way to prepare for owning as well, if you intend to do that one day. Don't know if you should use that one on your parents though!
My parent's let me share because they could see I wanted more involvment with horses than I was getting from 1 hour per week at a riding school. As much as I enjoyed riding there, I just wanted to do more. I wanted to be able to look after the horse more than a riding school environment allows, and have more freedom.