Theory No. 1
Irregulars don't just always OPEN the door. By opeing the door, it grants them special power. Perhaps in the real world, they are just normal people but because of determination or any other powerful feeling, they manage to open the door.
Theory No. 2
Those that are chosen for the tower are the exact same thing as irregulars, except their learning capablities are bigger. To qualify as an irregular, your life must have to be shattered by something that urges you to move on. I'd say that once you become a chosen one, your thought is just focused n winning, but those "not chosen" have a better urge.