For me, a "cull" is an animal that doesn't meet my breeding expectations. As a good breeder, you are always trying to improve, so you need stricter guidelines for the animals you keep. And you keep raising the bar of those expectations higher. Whatever you are breeding, animal produced should meet basic standards in color, body shape, QUALITY in appearance, look masculine or feminine for the species, be an improvement over parents.
You can't keep all the animals you have and produce. So with choosing replacement youngsters from each crop, you remove the less ideal older animals for various reasons to keep a stable sized herd or flock. With the older ones, maybe they don't produce twins, or calves don't gain as well in time allowed. An animal may just be old, not up to keeping themselves in good condition anymore. With sheep, when the teeth are gone, you need to remove the animal from the flock. Keeping old animals as pets is an expense most can't afford on the farm, with special feeds and care needs that take more time. You have to regularly replace bulls for new blood and because his daughters are going into the herd, so he can't sire their calves.
Horses can be a bit harder, but volume breeding requires gelding colts and selling on females that are not what you want, is required to prevent being over run with horses. Also gets your good animals out to be seen by other folks who might be horse shopping. You gain a good reputation for producing nice animals. We don't breed a horse often, we always plan to keep that offspring. However if that foal doesn't grow up to like driving, it must be sold. Like other activities, some drive and some don't. Perhaps a horse doesn't match our other driving horses in way of going or size, so he has to go. Driving horses is our main use for them, have others that both ride and drive, so can't keep a riding specialist. They sell to nice places, we get a good price, but of course not ever what you have invested. Just really hurts to sell with 4 years or more put into that horse and we really LIKE all our horses. We have limited space, so those who don't work out have to move on.
Same thinking with a calf or lamb crop, the young animals are part of the yearly cycle, selling them gets cash back into the budget, puts them into hands of people that will use them. You sure can't keep them all!
Culling can be hard, sorting down and selling them on, but is required unless you keep only pets. Pets cost a LOT in both cash and time, can really wear you down just taking care of them.