@just_ine - Many people confuse impact play with sadism. The key element of sadiism is as PurpleKnight outlined, obtaining pleasure from another persons suffering. If the masochist enjoys pain it is questionable if that is suffering. Your doctor analagy falls flat because the doctor does not get pleasure from the patient's suffering. Let's imagine he did. Would you be happy with a doctor who got (sexual) pleasure from the pain of patients. Would you allow him to treat children?
You stress consent but consent does not affect the definition of sadism. The sadist gets pleasure from another's suffering irrespective of consent. The only difference consent makes is it overcomes legal obstacles. Remove the legal obstacle and what do you have, a concentration camp guard. in fairness I suppose we could argue that without legal restraint all men would be rapists, but history shows us that most men can exert self restraint whereas that seems not to be the case for the sadist.
As to whether it can be taught, yes skills can be taught but not the pleasure. How does the sadist learn. He probably starts off tying tin cans to the dog's tail. It's a gradual process and he learns mostly from instinct and trial and error just as the school bully does. The screams of his victims is a learning aid for improvement.
I do not believe that bdsm should mean anything goes, there are some kinks that are indications a person should consider therapy. What does consent in the asylum mean? Nothing because the sanity is not there.