I think it's a common misconception among non-horsey people that riding is easy, the horse does all the work, and therefore there is not that much that you, the rider have to learn. Quite to the contrary, riding is hard. The horse may take the steps for you, but you have to be able to control your balance and control the horse all at the same time. Every part of your body -- your heels, your lower legs, your upper legs, your core, your shoulders, your arms, your hands, your head -- have to be able to move independently from one another, because each one means something different to the horse. It's a carefully orchestrated dance that requires precise coordination and takes many, many years to perfect.
And of course, horses themselves take work, too. If you lease or own a horse, riding isn't your only responsibility. Horses need to be groomed, see the vet and farrier, and sometimes they need to be cared for during illnesses or injuries that make them unrideable. They also require attention that has nothing to do with riding: bathing, blanketing, hand grazing and so on.
This all came up because the mom wanted her daughter to do a show this summer, and her instructor said she needs more riding time before she starts showing. Ideally her instructor would even like the girl to eventually lease or buy a horse for riding, lessons, and showing. Unfortunately, the mom has the daughter's schedule jam-packed with various summer camps (and extracurricular activities during the school year). I can't imagine cramming in another ride or two a week, let alone the time it requires to lease or own a horse! At some point soon, mom and daughter are going to have to sit down together and decide how seriously they are going to pursue riding, so that they both have realistic goals based on the time they are putting into it.