As a kid, gymnastics was a way to learn things. Not just skills, but things like "this is how to not annoy everyone on earth" (I was a really weird kid), that some things are more worth fighting for than others, that failure isn't the end of the world and doesn't have to be permanant, how to be a good winner, how to be a good loser, how to be happy for someone instead of jealous, and that impossibility is a temporary condition. Attention to detail, coordination (see again: weird kid), balance, poise, and the confidence that comes from doing crazy things in a leotard in front of a cumulative million strangers were other benefits. And we weird kids can be successful, socially and athletically, in gymnastics.
As a teenager, I learned to be a role model, & to evaluate my actions in the light of "there are kids watching who think they want to be just like me". There's so much that isn't even a consideration when you know that a little kid or 12 who you care about are going to follow your example. The pressure got more intense, but gymnastics was a way to learn to deal with it. It was my non gym pressure valve...a bad day could become a good day with some gym time. And it gave me a way to earn my keep--coaching was my first job.
As an adult, I'm still physically strong. I know that even out of shape, I can do things that most people I know wouldn't dream of attempting. Coaching allows me to pass on the gifts of gymnastics (and is my livelihood), & I know this makes an impact in the lives of shy kids, weird kids, short kids, girls who are growing up in a society that's not always awesome to them...and knowing that really, I impacted people I care about in a meaningful way, that's pretty awesome. Gymnastics is a tool for growth.
Gymnastics gives one a taste of flying, a taste of invincibility. Once you've been immortal, flown, and done the impossible, there's very little you can't handle.