Anger and hatred are both negative “false” emotions. Anger results as a result to negative experiences, but is it not a healthy or justified response. It is a coping mechanism to help you deal with loss or perceived injustice. The reason this helps you cope is that it directs blame at someone or something; it is easier to focus on what you’ve blamed, and focus on that to direct your feelings at, instead of dealing with how you feel. Dealing with pain by grieving is the only healthy way to deal with this, but since it is painful it is difficult, and easier to simply avoid thinking about it. Anger can easily turn to hatred and revenge, which are other coping mechanisms that make it easier to deal with the issue.
Anger is essentially a form of blame. The things people do when they are angry, or angry at someone are irrational and intended to make themselves feel better. Simply the thought of hating someone is enough to focus your attention away from your pain and instead tell yourself that its OK because it’s their fault. When you are angry at someone it is easier to hurt them as a form of perceived retribution, which serves to make you think there is justice for the injustice that was done. This is all a lie you or your subconscious tell yourself to feel better in the face of pain. This is done to avoid grieving by finding a target and redirecting your focus from your issues onto it as a way to fix your problems.
Anger, hatred, and revenge don’t solve your problems though, they create an artificial problem for you to solve. This artificial problem is easier to deal with mentally than having to think of your loss, which is the only way to grieve. Since the problem isn’t real, solving it doesn’t fix your actual problem of loss or injustice. The only way these negative emotions can make you feel better is through even more self denial.
As anger, hatred, and revenge are all forms of denial and escapism, what you feel after can only make you feel better if you convince yourself that they solved your problems. Once you have taken revenge and proclaimed that justice is restored, you should realise that having done a bad thing to fix another bad thing doesn’t make any sense, and more importantly does not fix your original problem or get you back what you had before. The only way this can make you feel better is if you cling onto it or convince yourself that those who do bad things deserve bad things done to them.
As none of these things are either logical, reasonable, or practical, what you end up with is denial, more damage done, negative emotions, and possible psychological issues. The amount of denial or twisting of morality and logic required to sustain these things are responses to trauma could lead to insanity. If someone is willing to forego the morality and logic they would use with other people for the exception of the people they hate and deem unworthy for the sake of how they feel, then they might as well forego them altogether to maintain that feeling.
All of this is caused by a coping mechanism because people do not know how to, or do not want to deal with their emotional issues. It is said that thinking about loss does not help anyone, but this is exactly the opposite. To overcome loss you must think about it, understand it, face the sadness, and grieve. Revenge is a petty excuse to avoid sadness.
The fact is that some injustices cannot be made right. Hurting others to make yourself feel better is selfish and unjustified. It does not matter how sad or angry you feel, inflicting pain on others like was done to you is similarly unjust and unwillingly makes you as bad as the cause of your own loss. Punishing someone only causes more harm. If you feel better knowing that someone is suffering, then you are lying to yourself to make yourself feel better, or you have a twisted sense of morality.
No one deserves to be punished, if someone does something unjust then they should be rehabilitated, not hurt. The only reason that someone should be hurt is if it is the best known way to avoid another, worse injustice than hurting them. It is easy to trick yourself into looking for someone to blame, and then twisting your mind to derive pleasure out of their suffering, or lie to yourself and say that justice has been restored. These are all easy, but they are not what you need. What you need is to understand your pain, not direct it at someone else, or lock it away, but become resistant to it. When you face your pain and eventually master it, you can be at peace with it. If you do this the pain will dissipate, and although the loss may always linger, you will be far better off.
Revenge will not take away your pain, you must master your pain to eliminate it thereby solving your problems.