Why would someone who is already in pain wish to inflict it upon others?

psychologically it makes a person feel better about their pain due to not being the only one in pain

People who are in pain often inflict it upon others. Pain takes away a lot of our moral compasses, leaving us with only the primal thoughts of the need to survive and take down others and make them feel our pain. We think that if other people were to suffer too, it would make our suffering lessen.

Sadly people in pain arent always aware how they may be coming across to other people. This is not an excuse or a reason but may offer some comfort. Would it help them or you to discuss the pain further? Maybe sharing your experience could help you develop / progress further?

There are a lot of reasons someone struggling would want others to struggle to. One could be to achieve a sense of revenge against the world. Another could be that they want to feel in control, like they can dish out what they are served.

As an empathetic person, this is something I have really struggled to understand. I have a good friend who opened up to me recently that she used to bully others when they were feeling vulnerable. My friend told me that when she felt really vulnerable, she wanted to feel like she could have some power-- sometimes power over other people. A lot of people in pain feel as though they have been wronged by other people, and as an attempt to cope feel the need to seek revenge on the people that have hurt them. Because they don't always have access to the same people, it can cause them to turn that frustration onto another target.

Because that someone thinks wrongly that transferring the pain will lessen his own pain, but the transaction of pain will only further multiply the pain instead of dividing it, this is the law of nature

Inflicting pain upon others, I think, is a way of trying to forget your own pain. It takes your mind away from what you might be going through, and it also gives you a sense of power over others. It can make you feel stronger, and like you can control something. Most of the time, people inflict pain because of their own insecurities and misery. And as sick as bullying is, and as much I hate it and want it to stop, I don't completely blame them.

Maybe they just want to take it out on others or just try to be cool/popularity or show off to there friends

Because to them, the others may have it better. and it causes them to desire that life, when they feel like they don't have it. So they wish worse on others to feel a somewhat relief

Because sometimes it's more of a subconscious thing, if I am feeling this, then you deserve it too... And of course that is not correct... And most of the time these people are not horrible... They just don't know any better... Don't know anything else...