It is interesting that the name "Endorphin" contains the letters "orphin" like in "Morphine". This was intended when creating the name "Endorphin" since it is somewhat similar to "Morphine" in both chemical and metabolic respects. Endorphin can be released in when pain is experienced. So possibly we are having a pleasant experience when relaxing into pain during a pin in Aikido that is similar to the one when smoking opium. Still the problems caused by addiction to opium seem not to be present when doing Aikido. And certainly many other facts are important. So saying we just are addicted to Endorphin is far too simple, but an effect one should consider too.
I think it's also too simple because, if I understand correctly, exercise-related endorphin production doesn't just happen as soon as your body is under stress -- it's got to be strenuous and it's got to be prolonged. I suspect that for the large majority of people, the feeling of well-being that they come to experience during exercise, once they've been on an exercise program for a while, is mostly the body's becoming better conditioned and more comfortable with the stresses of exercise. That, plus the other general physical benefits that come from or often accompany an exercise program -- better sleep, improved circulation and respiration, better eating habits -- is more than sufficient to account for exercise starting to "feel better" after you've been doing it for a time.