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

Because it makes someone feel better about themselves. And it will make others feel better about themselves also.

It can be due to many factors. One of which can be anger this means that the person could have anger issues and their only solution is to hurt others instead of finding a solution. Best thing to do is to tell someone so you are safe from any pain or suffering

To some individuals that pain that is inside them is to much and they need to get it out. Sometimes that is to themselves other times, it's to others. Sometime they see similarities between themselves and other individuals and makes them want to lash out that way. Sometimes it's because they are envious or jealous, or believe that if they are in one way/state others need to also. There are loads of reasons why.

Because they want someone to be able to understand whatever type of pain they are going through, be it emotional pain or physical pain. And sometimes some may do it for revenge.

Because they want others to suffer like they did. It's a very selfish action, but sometimes people are just so broken that they'll make mistakes they're gonna regret later. For example, if someone stole your favorite teddy bear and threw it away, you (may) would want to throw everyone else's stuffed animals away too, because you're sad you lost yours.

It can be a matter of feeling greater than they are, that is sometimes when someone is in pain they may feel weak and to reverse that they'll make someone feel inferior to them.

Pain can be caused by so many different factors. If it is an external factor, people may be less likely to strike out against other people. However, this could also teach this person to be aggressive. Internal conflicts are the stereotypical bully who doesn’t understand themselves, so they act aggressively towards others.

Someone who is already in pain wish to inflict it upon others to make others feel bad about a situation only to make themselves feel better at times.

Because they want to make that person feel what they felt. There could be jealously involved that this person hasn't experienced what they went through. They want to inflict that pain to see the reaction how it might make them feel.

Have you ever heard the saying 'hurt people hurt people'? By inflicting pain on other people they are projecting their own unhealthy feelings onto you because they are not in a place where they are able to communicate healthily. The hardest part is being on the receiving end of this treatment but you have to try really hard to not take it personally. Because 9 times out of 10, it's not about you, it is about how THEY are feeling. If it's someone you really care about and want in to keep in your life, try and get to the bottom of their behaviour. Maybe ask them why they feel the need to hurt others (remember to approach with sensitivity and zero judgement). If this person isn't dear to you it is best to remove yourself from the situation as you hold no responsibility to them and your mental being and happiness comes before anyone else'.