Why does Jesus ask us to forgive without limit? Not seven times, but (depending on your translation) seventy-seven times or seventy times seven times? A number that signified infinity. Because it is the right thing to do? Because it is the model that our Lord showed to us in forgiving those who crucified him? Because, it is the model that he showed in offering his life for our sake?
Yes, but also, as with so much else that God asks us to do, because it is good for us.
When someone wrongs us, they commit an injustice against us. Justice requires that they then owe something to us. They are indebted to us because of what they have done to us.
When we forgive, we do what the king did originally. We release the debtor from their debts. We let go of what they rightly owe to us.
Perhaps more importantly, we move on from the injustice that had been committed. Rather than retain an accounting of the offenses committed against us, we turn away and move on.
Does the one forgiven even care that we forgave? Perhaps not. Whether or not the offender feels released in being forgiven, the reality is that the offended person is released by forgiving. They can put down the burden of any resentment or anger that they might have felt. And, they are able to get on with their lives.
Will the one who forgives completely forget what was done? Likely not. Will they necessarily restart their relationship with the one who offended them? Prudence might dictate otherwise. But forgiveness allows healing to replace resentment.
In our relationships with others, forgiveness benefits the one who forgives. Perhaps much more than it benefits the one who was forgiven.