Three reasons:
First, I think gymnastics is an incredibly powerful tool for building young people into stronger, happier, healthier people. Physically, it makes the body stronger, more agile, more capable in just about any activity. Mentally, it teaches skills far too numerous to list.
Second, I love love LOVE the technical challenge of breaking skills down and figuring out how to train them efficiently. Every skill is a puzzle, and once you solve one puzzle you can use the pieces to help with other puzzles. Sometimes you go back to an old puzzle you thought you solved and find a new solution. It's all puzzles and optimization challenges, and I'm a nerd who grew up playing Zelda, so I love puzzles and optimization challenges.
Third, I find the mechanical laws underlying gymnastics to be sublimely beautiful, and gymnastics is to me an almost spiritual way of communing with the natural laws that govern the world around us.