Wanting to hurt someone who has hurt you is somewhat a natural defensive response. Many people choose to rationalize their thoughts and decide against revenge, which can actually be way more harmful than just trying to heal and move on from the situation. The people who choose to seek revenge prehaps do so because they think it will make them feel better and they don't care or haven't thought about how it could actually make things worse.
I don't think revenge is really sweet. If it is, it's an artificial sweetener. It does feel good to get back at someone, but the feeling doesn't last. We usually feel good right when it happens, and then we feel bad. Like a diet soda, I guess. It's sweet but not satisfying.
The few people that I have known who desired revenge, seem to base their justification on some presumed idea that they were owed something. Usually the "revenge" sought was somehow related to addressing a presumed injustice. In my opinion, revenge is never sweet because it rests on the assumption that the personal standards should be accepted as universal. This viewpoint suggests that the individual has some secret access to the universal good. Such a viewpoint will eventually be unsatisfactory because it doesn't allow room for personal growth. Society and social systems seek to find ways to develop collectively while maintaining the growth of the individual. One of the flaws in our present legal system is the emphasis on punishment instead of justice which would address the needs of the victim as much as the action of the violator.
In the day as a junior high teacher, I had the opportunity to witness many "social injustices" in action. It was always interesting (and satisfying) to see potential conflicts be looked at from both a collective and individual point of view. The incident that occurred was discussed in public discussion, and the parties involved allowed to "state their case". When the discussion was concluded, neither party seemed bent on revenge, and usually a deeper level of appreciation of the community was demonstrated in renewed cooperation.
The personal need for justice is something that is inherent in most men and women, and when one suffers an injustice, there is a natural urge to make the situation right. This is often a reason for revenge. Reversing the injustice in some manner can be highly fulfilling, thus the term "sweet revenge."
However, vengeance is often looked upon as a harmful and unethical act, since the goal is often to inflict greater punishment to the person who committed the original wrong. Personal vengeance also goes against the true meaning of justice, when punishments are handed down in a legal fashion. Nevertheless, revenge can be sweet, especially in literature, as evidenced by Montresor in Edgar Allan Poe's "The Cask of Amontillado," who enacts the ultimate revenge--murder--upon the man who had "borne" him "a thousand injuries."