Why do people who get bullied bully other people? Why do some people think it's okay to take it out on others?

Because they are afraid of getting bullied themselves so they try to display their dominance first. People can't accept who they are so they feel like they have to do something to forget that. Lack of attention amongst themselves can also lead to bullying. If they never received proper attention, they will do anything to deserve attention. Perhaps they lack the understanding of social equality and they desperately need some help. They want a response from you so they can keep on patronizing you. Just ignore them and keep on walking no matter what they say. Opinions are opinions and everyone has them, it doesn't mean that they are true. Bullies have to bully because they don't know any other way to get attention. It's up to you to be the mature one.