Wrath would be another level deeper than hatred in that it is closely synonymous with being homicidal or in a rage that is directly related to anger towards someone or a group of beings.
Perhaps wrath could be directed towards a shark that ate your spouse or towards someone that, for example, raped your young daughter.
The latter example seems more poignant for an emotion of wrath and society, generally, would probably not fault a parent for killing a child's rapist if that can be proven to be the case and the wrath is taken out somewhat soon after the victimization takes place.
Wrath is considered one of the seven deadly sins because it harkens to our most lawless and base aspects as a species.
In some cases, wrath is wholly inappropriate and unjust. In certain pacifist philosophical viewpoints, wrath is never appropriate where it acts out violently. Most people, not being pacificists, would deem certain sitautions wholly appropriate for wrath.
If one is being executed by a tyrannical regime and one can, in a sense, go into a Rambo-like rage with various assault weapons against such a regime to save one's self and others who are being victimized unjustly, then most people would not see this as wrong.
If, for example, Jews in Nazi Germany were capable of arming themselves and fighting back against the Germans, most people would not blame them for any carnage that ensued.
My focus here is on the emotional state of wrath and why it is such a negative emotion, even in cases where it is justified. I am less concerned with the circumstances of the wrath than I am with the way it makes an individual feel. As a human male, I have perhaps experienced wrath, to some degree or another.
Again, whether justified or not is beside the question. It is an all-consuming emotion that eats away at he or she who possess it. It can not typically be quenched unless the focus of the wrath is utterly destroyed. This destruction, even, will not necessarily solve the problem of possessing this emotion as it will be difficult to extinguish once let loose on reality.
Wrath can be useful in war and in self-defense. Wrath takes hatred and enlarges it to the size of the sun and, if not handled properly or in the right situation, wrath can become an all-consuming negative emotion that leads to unbridled wrath- a state in which those not justifiably the focus of the wrath become innocent victims or bystanders of the emotion.
In most societies, wrath is never healthy unless that society is so sick that it needs to be purged of large segments of itself.
Nations that commit war crimes and murder their own citizens in cold blood are certainly, I think none would argue, ripe for wrath from within to cleanse the system that allows for such heinous acts. Wrath can be fed into a being. Wrath can be removed with care and kindness.
A dog can be made to be wrathful if mistreated as can a citizenry be made to become bloodthirsty if it sees itself as oppressed to the level of murderous tyranny as some do in some societies throughout history.
All oppressed people have every right to feel wrath against their oppressors but, once vindicated or relieved of this oppression, wrath can easily spill over towards those people who do not deserve such demonizing.
Wrath is dangerous and negative, but, I would argue, a perfectly human emotion to have towards any who unjustly rape or murder innocents.
Wrath has no use for peace until the focus of the wrath has been exterminated.