An animal's tail is an extension of the spine, and is extremely sensitive. Twisting, pulling or raking a tail back and forth over a fence is extremely painful for animals, and that is why the Rodeo Mafia likes it.

Tail twisting is used carefully and sparingly by veterinarians to move large animals. Rodeo people use extreme tail twisting to force tame, domesticated animals to act "mean" and "rank."

Tail twisting is mainly committed against calves and steers to make them run from chutes. However, all rodeo victims, including horses and bulls, may fall prey to tail twisting, raking and pulling. 

You can see some tail twisting in both of these videos: