To me, when a child bullies or is mean to another child, it means the bully does not respect themselves or anybody else. Children are not born respecting themselves. They learn it from their parents and siblings. If parents treat their children with respect, the children learn to respect themselves.
By the same token, if parents are mean to their children, the children will be mean to other children at school. If parents hit their children, those children will hit other children. Bullying is not natural. Bullies are made by parents who are bullies.
However, parents are doing the best they can. People tend to learn how to parent from their parents. So, if the child is disrespected or bullied by their parents, they will grow up to bully their children.
Many parents are on alcohol or drugs. Usually this indicates a severe lack of self-respect and results in the parent being mean to their child. Also, parents who are stressed (like not being able to get a job) may express their stress as meanness towards their children. Either of these situations will lead to the child becoming an addict and/or a bully as they grow up.
Parenting is probably the most difficult job I've ever had. I make mistakes. I do try to respect my child's opinions and explain why a choice might not be the best one. I think putting the child first in every way will go a long way toward letting them know we love them and they are important to us. I believe if we all try hard to be attentive, loving parents, we can eliminate bullying.