I saw it as Dumbledore having chosen what persona to cultivate in order to best get away with his actions. Take, as a representative problem, that he has to make sure Harry carries his father's rock. He could try to assert authority and order it, but that would make him be seen as a tyrant. He could try to invent a good explanation, but he probably couldn't actually convince Harry, since he can't give the true reason and there isn't actually any other good reason. But by playing the benevolent eccentric, he can get Harry to humor him with minimal harm to his reputation.