Cherie is spot on. As to the horse training part of it, trainers are just like any other profession. You have those who are working hard to do it right, and those who are concentrating solely on what makes them money.
Originally, the cutting horse was the highest level of cowhorse on a ranch. He was used to sort and separate pairs (calves from cows) before pens were common. There would be a main herd containing pairs and then a smaller herd would be formed that contained the freshly separated calves.
Of course, this method is pretty well never used anymore, but we can certainly see how neighboring ranchers would have pride kick in and start betting that their horse is better than your horse and bam, the first cutting was invented.
Cherie is spot on with the rules and regs.
I have made my living as a 2 year old man for nearly 20 years. I put the first year on these prospects. It takes 18-24 months to train one and they generally begin showing in the futurities at the end of their 3 year old year. Many, of course, have soundness issues and things and don't finish their training in time to compete.
The age events are where most of the money lies in competing. Futurities are for 3 year olds. 4 year olds show in Derbies, and 5-6 year olds show in Classics. Just about any horse that you hear of that won 6 figures in cutting did it in aged event.
As Cherie said, the aged events are big productions that can last a few weeks. There are also some smaller aged events that will be held in conjunction with weekend shows, but they typically don't pay nearly as well, and aren't going to be nearly as competitive as the big shows.
Cutting is now all about showing what the horse can do, but there are still many side benefits. Nearly any cutting horse training operation also doubles as a cattle backgrounding operation. Personally, I do not take in cattle from order buyers as many others do. My typical set of heifers are replacement heifers that I am using to train my horses, but I am also getting them gentled and easier to handle for the cattle producer. How you handle cattle makes a tremendous difference in the way they work. You can indeed spoil a herd and make them nuts, but you can also handle them so that they become well settled and are calm and easy to handle. I even get in some sets of wild a$$ marsh cattle. When they come in they jump fences and run wild. Most of the time, I could drive them down mainstreet by myself after a month or so. I also have always used my 2 year olds to do as much of the ranch work as I can. So, my 2 year olds also rope and doctor cattle and I use a different one each day to pen up the heifers that I am going to work.
There is absolutely no reason why these horses need only by specialized arena babies. It aggravates me to no end when I see an older trained horse that is useless to use to pen up the herd before working them. There's just no reason why that should be. No reason why working cattle a horseback should make them harder to work again. True, they will have a smaller bubble, but they should still honor a horse and be moveable at a relaxed speed and any direction I ask.