In my experience, people often conflate forgiveness, reconciliation, and redemption. They are distinct things. People also often do not understand the role repentance plays (evangelical Christians are _especially_ prone to miss it entirely).

We can forgive someone for horrific things they've done, even when they are utterly unrepentant. Forgiving them is changing our attitude about the harms the offender did from anger and hatred to acceptance and peace. This does not mean saying "what they did was okay," but rather accepting that they chose to do something horrible, learning to make peace with their hurtful choices, and focusing on healing the damage to ourselves and others rather than seeking to injure the injurer.

Reconciliation is mending a damaged relationship between two (or more) people, as much as it can be. Unlike forgiveness, true reconciliation requires that all parties make an effort - the injured party must put in the work of forgiving the offender, and the offender must do the work of repenting.

"Repent" now means "make a show of acting sorry" in evangelical Christian circles, but genuine repentance is very different. It is recognizing the harmful choices you have made and truly regretting them, and as a natural outgrowth of that regret, choosing to do what you can to heal the damage you have done. It means accepting the consequences of your choices; a repentant offender expects to be distrusted and treated differently for their crimes, and does not resent it, realizing the shattered relationships (emotional, familial, civil, and otherwise) are part of what they chose. Without repentance, others may forgive an offender, but reconciliation is not possible - if the injured continue a relationship with the aggressor, it is necessarily a stilted, broken, fragmented one.

Redemption is rarer and harder to achieve than either forgiveness or reconciliation. It is when reconciliation succeeds and goes beyond success, giving birth to something fuller and more beautiful than what was first broken. Adapting the words of my lost-yet-beloved faith, "He will wipe away every tear from their eyes, and there will be no more death or sorrow or crying or pain. Behold, He is making all things new."

This is not, in my experience, how conservative Protestant evangelicals use these words. However, in the decades I practiced Christianity, I slowly found these ideas in the Bible, despite the ludicrously-wrong exegesis practiced in US churches, by reading the texts many, many times. I find a great deal of truth and wisdom in them, considered this way. I hope perhaps my explanation can help you understand why so many people resonate with the message recorded in the Gospels, and the one that Dostoevsky so loved.