I always tell my kids, it takes 100 falls before you're considered a great rider, so most of them count backwards from one hundred. Thankfully this gives them plenty of time before they become invincible.
There's always a risk when riding a horse, the trick is to know when your in real danger or when your nerves are getting the best of you. Horses are large and sometimes unpredictable but under the right instruction there is no danger. Most riding facilities will ensure they have "bombproof" horses, meaning they are quiet and easy to control. Once learning all the skills required to ride a horse, it is then safe to move onto a horse considered slightly more "green", meaning it has received less training and is slightly more unpredictable.
In the horse world one of the greatest struggles is to watch a "green" rider on a "green" horse. This can be a disaster waiting to happen or simply just the wrong fit. A rider will sometimes not have the experience needed or the knowledge gained to be riding a horse that is still learning and impressionable.
Not all horses are well behaved, but in the right hands and with the patience and consistency needed, they are happy to listen and obey. Horses are meant to work as one, to become a team and to co-exist. This is a fact that is commonly forgotten by inexperienced trainers and riders and can result in harmful ways and dangerous situations.
George Morris is an Olympic rider, trainer and in the past several years a host of clinics to riders of all ages. He is a legend in this sport and apart from having a wealth of knowledge he is known for his blunt comments and witty nature. His teaching follows a lot of principles that I value. To some they are harsh, but the underlying meaning is to realize your own faults before assessing the horses. A lot of weakness comes from the rider first and is due to a lack of invested discipline and motivation. I will leave you with some of my favourite quotes from Morris himself.
"Is that clapping? I hope your clapping for the horse because the rider doesn't deserve it."
"The best exercise for your riding? Put down your fork."
"You either go to the hospital or get back on."
"Distances are like men. Never take the first one you see, there will always be another one."