I have trained to Rear, bow, and wave. It is dangerous (and so is Cross Country) and there is a mile-long list as to reasons that I might not teach it some of which others have mentioned. There is also a mile-long list of requirements that I would have for a horse before teaching to Rear at liberty.
Mine are VERY well mannered on the ground and stay OUT of my space. When I ask for the rear, they are to quietly brace themselves, back a few steps if needed, shift their weight to the hindquarters ( I do not teach them to rear up wildly and striking but as the Lipizzaners and balancing their weight onto the base of the hindquarters) and raise their front end WITHOUT any striking. They tuck their legs under them safely and then back down, happy and looking for a treat. I have never had problems teaching this or have had any aggressiveness issues but it's not something anyone should teach.
Young Lipizzaner stallions begin Dressage training at age 4, and are not considered finished until the age of 16 years old. Their training is done by professionals and the trainers take their instructing very slowly and seriously!
