How did you handle the situation when you disagreed with a superior?

Your superior's Word wins. Having made your case, you respectfully concede and do whatever it is his way. (That way you keep your job, even if you don't want it at that moment.) If the subject of your disagreement violates your sense of right and wrong, then start looking for another position while following his/her ruling. This has happened to me, and you hold your cards close to your chest and make a plan for your exit.