Do you think people who were bullied in school and at home end up being bullies when they grow up?

I saw the Timothy McVeigh tapes on MSNBC. It was very interesting. McVeigh was badly bullied in school. But, as a soldier in Iraq, he had problems with the fact that he had become the bully. He had some major post traumatic stress as a result. He just had problems with the fact that he killed not only Iraqi troops, but he also had killed regular people in Iraq, as did many troops because war is messy. So what happened? McVeigh comes home and has PTSD and then ends up becoming the ultimate bully by bombing civilians in Oklahoma City. It's all quite confusing. So, do the bullied usually end up becoming bullies or do they speak out against bullies when they become older?