You might be better off to leave the diagnoses to those who are qualified to make them.
According to experts, people who bully others may:
• be in schools where conduct problems and bullying are not properly addressed.
• have been bullied in the past or currently.
• have come from families where the adults are overly lenient or where there is low parental involvement in their lives.
• have come from families where there is bullying, aggression, or violence at home.
• have experienced being excluded, not accepted, or stigmatized at school.
• have feelings of insecurity and low self-esteem, so they bully to make themselves feel more powerful.
• have parents and caregivers that do not provide emotional support or communication.
• have parents or caregivers who respond in an authoritarian or reactive way.
• not have skills for handling social situations in healthy, positive ways.
• not know how to control their emotions, so they take out their feelings on other people.
• not understand other people's emotions and feelings.
Now, the mere fact you may understand these reasons does not mean you are required to feel empathy for bullies.
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