Warning, long post!
It's a great question, and to me it's not so much that one is right and one is wrong, but each lead to different consequences within yourself.
But moreso the important thing I reckon is where it is coming from. 'Settling the score' and 'forgiveness' are coming from two different levels of consciousness.
Settling the score there's an inherent belief that the other person deserves it, but it's moreso the 'juice' that you get out of it which drives it. The juice of righteousness is a really sticky one.. and it's what many people are addicted to as a lifestyle. The ego (in spiritual parlance and meaning, not the psychological one) loves nothing more than to be right.
The level of consciousness which needs to 'settle the score' comes from a place of belief in punishment, and it's actually a way of them punishing themselves, because you're giving reality to the idea that you were a victim. Btw this isn't at all saying that criminals etc don't need to be jailed and we should all forgive and la-di-da let's all hold a hands and travel the rainbow journey haha.. that's the appropriate response to keep citizens safe and potentially bring about some level of ownership for and honesty for the person about the crime. I'm talking about the inner world, rather than a utopian world ideal.
Settling the score there's a belief in there that not only IS there a score to be settled, but that doing so will make you safe, happy, fulfilled. It's driven by an energy of vengefulness, aggression and antagonism.
Forgiveness comes about only through willingness to let go of the juice of being right. Because you see through that need, and see that being right never fulfils you.
You're essentially releasing energy of the 'past', freeing yourself of it and subsequently your feeling and sense of freedom emerges as you realise this can be genuine way of living.
It has a simplicity to it, but doesn't make it easy haha... The reinforcement of certain habits can take a bit to break down... but only a little willingness is necessary.
Forgiveness realised and admits that the human being is fallible, and not perfect. It requires an inner honesty. And alot of people think that forgiveness is you forgiving truth, but forgiveness actually relates to error. You're forgiving/overlooking the other person's perception, and also your own. Understanding that people are simply operating from their perceptual worldview, and you're forgiving that, and more importantly you forgive that within yourself. You look beyond error and you don't make it real.
"Forgive them, for they know not what they do", is seriously profound and really encapsulates that.
And the person who mistreated you actually feels the pain, and will experience the consequences daily as to what lifestyle they lead. Call it karma or whatever (which isn't a reward/punishment system in my understanding, but simply sequential and natural consequence). In other words, chances are the people that go around intentionally harming others are harming themselves on an exponentially far greater level, and may feel tortured and unloved every single day, until there comes a time of willingness where they don't want to do that anymore to themselves. And by committing yourself to certain lifestyles you naturally attract situations which will bring up facing that directly, to either reinforce it or transcend it.
But this doesn't mean you are naive and don't call other people up on their stuff (from how you currently understand it). Accountability and responsibility I think are still incredibly important. It's just letting go of the juice of righteousness, realising everyone is doing their best at any given time with how they see the world and others, and how people treat others is a reflection of how they see and treat themselves on some level.
Forgiveness is actually more to benefit yourself. It releases you from that person/situation, and releases the world from your imposition of needing to be in the right. Which actually lightens and helps the world.
And another thing to add is that some have a very strange view of forgiveness... and actually use it AS a tool of righteousness. That: "I'm willing to forgive you as you did did evil." Forgiveness can be used as a weapon of judgement, whereas it's true purpose is to release you from judgement.
Just all food for thought!
Some great quotes from a teacher I follow David Hawkins:
"Compassion and forgiveness do not mean approval."
"The willingness to forgive others is reflected in our own capacity for self-forgiveness and acceptance."
"From previous studies, it was learned that everyone is born under optimal conditions for karmic opportunities; therefore, it is wise to judge not, for what appears as misery or catastrophe may be the doorway to liberation for those who have negative karma to undo. Thus, seemingly catastrophic events may be the very essential and necessary elements for the evolution of the soul."
"Guilt is the consequence of the memory of regretted past actions as they are recalled. These can be transcended only by recontextualization. Mistakes are the natural, impersonal consequence of learning and development and therefore unavoidable."
"The past cannot be rewritten, but it can be recontextualized so as to be a source of constructive learning. Regret over past events or decisions can be ameliorated by realizing that they ‘seemed like a good idea at the time’."
