Generally speaking, people who bully have a desire for power, respect and control (many of these things aren't present in the home environment). Also people who bully may have low self-esteem and lack confidence; they try to build themselves up by tearing others down.
People who bully use fear tactics to repeatedly remind their victim that they are in control. When their bullying behavior isn't addressed they begin to think it is okay. There is no consequence for their actions and they're getting away with it... That is why it's so important for victims to tell someone and get help. Equally important, bystanders need to speak out when they see someone being bullied. The message needs to be loud and clear --- Bullying is not acceptable.