It seems like a simple question, but the answer is very complex. Since there really isn't a single cause of bullying among children, one cannot just give an easy answer. There are many factors to consider including the child's family life, peers, school, television, movies, video games and community factors which individually, or collectively can contribute to a child's likelihood of bullying.
Punishment should not be the end all solution. The child maybe a victim of bullying themselves, abused by their parents, family members, older siblings, peers, etc. I don't believe children are born bullies, but I'm more inclined to except they are acting out some sort of physical, mental or emotional abuse they are going through in their own lives. This may not always be the case, however, we can't ignore those possibilities.
Also, there was a new study that said that children who bully are at an increase risk for anxiety, depression and eating disorders. Researchers found that bullies are more likely than their classmates to suffer from low self-esteem, depression, and behavioral problems from early childhood and through primary school, and are more likely to suffer from mental health problems later in life too.
Dr. Leslie Gutman, lead author of one study, believes that schools need to teach that bullying is unacceptable and hold perpetrators to account for their actions, but also feels there should be greater awareness of the wider consequences and causes of bullying behavior.
Charlotte Lankard, a licensed marriage and family therapist in private practice believes bullying behaviors are nothing more than coping mechanisms, and it is our responsibility to teach kids how to properly handle situations instead of acting out against others.
Punishing and shaming is not the answer. Perhaps the bully is being abused emotionally or physically at home or is having trouble learning in school. Perhaps the bully doesn't have anyone positive in his or her life to guide the child in the proper direction. If we want to do away with bullying, perhaps we would be wise to see the boy or girl who is acting out through such behavior as someone who needs help, and offer instruction on more effective ways to cope.
What I can say is that we need to realize that the underlying reasons behind why a child resorts to bullying needs to continue to be carefully explored and examined for us to be able to fully understand bullying in it's entirety, including the best ways in dealing with it. The stereotypical image of a school bully as tough and self-confident needs revising because bullies are more than often victims too.