The allure of riding horses isn't just in the riding, though. There's the added bonus, and responsibility, of the other living, breathing creature that completes the equation. For girls, the additional duties around the barn are as much a part of the sport as the activities in the arena. It promotes healthy relationships, both with animals and other people. The effect can only be magnified with an animal as large, and yet fragile, as a horse.
Riding can have a protective value to teenage girls.
You'd be hard-pressed to find a young girl anywhere who won't profess to love horses, but the ranks definitely thin as they get older. For some, it may signify that a phase has passed. For others, it may be a concession to the considerable expense and impracticality of keeping a horse. I don't think kids who quit riding actually outgrow horses. I think they bow to family or societal pressure and realistically confront limited financial resources.