A two year old's joints will still be maturing and susceptible to overwork. While the hardening of the joints in the knees are considered a sign of physical maturity it's worth considering that joints throughout their bodies mature at different rates. While legs may be ready, hip and back may not. The horse owner ultimately decides how old a horse is before it goes to work. Thoroughbred race horses run as two year olds whereas other breeds like the Icelandic Horse are traditionally left until they are five or more years old.
Two is also the age at which horses are beginning to mature sexually although this varies between individuals. At two (or younger) a young stallion may be capable of breeding mares resulting in unplanned foals. If it hasn't been done before this point young stallions may be gelded. Mares too are sexually mature somewhere between their first and third year depending on their environment.
Mares and stallions should have to prove their worth before they are considered as breeding stock. Breeding stock should be carefully chosen for outstanding conformation, performance and temperament. The future of offspring also needs to be carefully thought out. Having foals for the sake of having foals, or because no one noticed an un-gelded colt pasture breeding mares insures a good supply of unwanted horses.
A two year old should have excellent ground manners, including loading onto a trailer, whether the next step to riding or driving will be taken sooner or later. A two year old can be lunged, ground driven, round penned, driven hitched to a light vehicle, and at the owner's discretion, ridden.