Jacobtk, I'm going to skip right to the source on this. The need for forgiveness is entrenched in the single most important Law in the world, the Golden Rule:
"Do unto others as you would have them do unto you."
This rule appears in every culture on the planet, from Christianity to Stone Age religions in the Pacific Islands. The core of human interaction and survival is reciprocity. The Golden Rule.
I think the quote you included above ("Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost.) is simply the Golden Rule, reworded. Forgiveness is not something we give up, or that is taken from us, it is something we give voluntarily. The Golden Rule says the rest. If we forgive those who wrong us, it may lead others to forgive our wrongs to them or other people who have wronged them. This builds harmony.
Self-forgiveness is just the extension of the Golden Rule to apply to the self. For me, self-forgiveness meant forgiving myself for all the terrible things I did to other people, and, (and this is important)all the terrible things I did to myself before I recovered from my abuse. By forgiving yourself you are at peace and you no longer blame yourself for failing.
As to why we should obey the Golden Rule? The answer to that question is the Secret of Life. By that, I mean I don't know. From a purely "Human" perspective, I think spreading love is preferable to causing hurt. Spreading love encourages harmony in human relationships, and harmony brings Peace. And Peace is our ultimate goal as a civilisation.
To answer your question, I think the benefits from Peace are far greater than what we give up when we forgive. Peace is the ultimate goal of humanity and it is what we are all aspiring to achieve. There is no higher calling, nor is there a more rewarding endeavour than the achievement of the day when all people live in a world of Peace, Hope and Love.
Nobby