Stand up to a bully and he will run from you
This reasoning works on the assumption that bullies are looking for victims, not a fight. Bullies practice their art every day. They are used to fights. How often do you practice standing up to a bully? A dedicated bully knows his or her trade and has no scruples about fairness. Just because a bully a jerk does not mean he or she is stupid. In addition, many bullies have had some martial arts training.
Even if you obviously outclass the antagonist, he or she may have a weapon, steel-toed shoes, or friends. If you do take on a jerk, win or lose you must remember that it will not end there. If you lose, it hurts and the antagonist now knows he or she can win and will continue to make your life miserable. If you win, the bully will be back again, this time with a weapon or with friends.
Even considering all this, standing up to a bully may still be the best thing to do, but not because the bully will back down. If the bully learns that every time he or she messes with you that, even if he or she wins, you will not submit to the bullying, the bully may decide to move on to a weaker target.