When I rode for Bill Hunter in high school, he told me there are two types of cattle - movers and shakers. The movers will try to sneak by you on the outsides, so will get a bit of running in as they try to circle you. The shakers are the ones that hunker down and do 3, 4, 5 quick rollbacks in a row as they try to bamboozle your horse into falling behind. Ideally, you want at least one of each during your run, to showcase your horse's ability to handle either type. A good cutting horse is "a mover and a shaker" meaning he can keep up with whatever the cow throws at him.
I'm adamantly against cutting horse futurities where 2 year olds are expected to cut … that is too much for young bodies in my opinion. But I really really love the sport of cutting as a whole, the idea of it, and riding a good cutting horse is definitely an experience everyone should have at least once. There is something supremely awesome in dropping that rein hand down on your horse's mane and telling him "Okay dude, it's all you now" and feeling him really MOVE to get after that cow, all on his own, because he wants to. I just love it when they get pinny eared and stare down that cow like they're gonna eat it alive if they get half a chance. Mm, baby. That's some sexy stuff, right there. In my opinion there isn't another sport in the horse world where the rider gives over complete control to the horse like that, where the horse becomes the 'brain' so to speak and the rider becomes, for all intents and purposes, an ornament.