But hurting someone is wrong, isn't it? Doesn't society condemn me as a Bad Person if I deliberately hurt people, and even more so if I enjoy it?
Before you get the wrong idea, let me clarify.
"Hurt" is a term used in this case to describe a sensation of physical pain. That's all it is: a sensation. A nerve response to a particular stimulus. When you remove the stimulus, the response stops and the hurt ceases.
For example, reach over and pinch yourself on the back of your own hand. If you do it with much force, it will hurt. Now let go. Unless you really put a lot into that pinch, the hurting stops. A strong pinch might briefly leave a red mark on the skin, but that is the extent of the "damage."
Now think back to a time when you've gotten your hand slammed in a door, hit your finger with a hammer, or some other sort of "pinching" movement. (You can go do this to yourself if you really want to, but I don't advise it!) Do you remember how badly it hurt, even after your hand was freed / the stimulus was removed? That was because your hand had been damaged and would take time to heal. You had gone beyond Hurt and into Harm.
"Harm" is a different matter entirely.
Martial arts, at their root, are about preventing hurt or harm to those you are protecting (including yourself), sometimes by inflicting hurt or harm onto someone else. Let's face it, even the term Martial Arts means "the arts of the ancient Roman god of war, Mars" -- the art of warfare, on whatever scale. Yes, martial arts can be used for the pursuit of enlightenment, self-knowledge, self-perfection, and many other things, but even many of the "softer" arts like tai chi can still be put to devastating use if applied in certain ways.
If I am practicing a particular martial art for the purpose of defending myself, I need to know if I'm doing the techniques in an effective manner. The only way I know of to be certain of that is to do them on a partner and judge how it affects them.
But if I harm my partner today, who am I going to train with tomorrow?
So when we train with a partner, we train to hurt them -- but NOT to harm them. This lets us practice the techniques, find the subtleties that make it most effective, and let our partner train ukemi (how to safely receive the technique) as well.
My goal therefore should be to hurt my partner without harming him. Likewise, if he hurts me without harming me, he has succeeded, too. That's why I like hurting them, and like when they hurt me -- because it means that we've both done our techniques correctly AND with a proper level of control.
I explain to every new student before their first class about the difference between hurt and harm. I tell them that there will be a lot of times in or classes where they will do things that hurt...
... but I will move Heaven and Earth to keep them from coming to HARM in my class!
Okay, we've talked the talk, now let's go walk the walk.