I've never really understood forgiveness. It doesn't make much sense to me, and seems inherently untruthful. I mean, either what a person did hurt you, upset you, etc, in which case that doesn't change- they'll never not have done that- and forgiveness would deny and negate that, or else you weren't really too hurt in which case what is there to forgive? Either you're deluding yourself (or admitting in the original case you made a big deal out of nothing) or else it's a non-entity from the start. I see forgiveness as linked to forgetting (we do say "forgive and forget" as though they are almost synonymous), and I don't forget my emotional responses. This is not to say that you should continue to relate to people in the now as you did then- to remain angry or upset with them as an overall means of relating to them when they can move on, change, grow, take responsibility and reflect, isn't viable, so long as any new moments with them evoke different emotions.
It isn't (for me) a case of "moving on" or "putting things aside", it's simply a case of not letting one moment or happenstance control you when there are others to take into account. You have to relate to people in the now, and as time passes people change, reflect, learn, reconsider or at least are available for the establishment of a relationship that differs from the one you had before.
I suppose I don't believe in forgiveness, because to me it requires both forgetting and a willing desire to negate and dismiss your own feelings, but nor do I particularly need forgiveness, at least how I define it, because I don't experience hate. If there is no desire for revenge (and I never experience that, either), and nothing stopping you relating to someone differently if they change, grow, reflect and learn, what possibly need is there for forgiveness? If someone hurts or upsets me, while it may take some (often relatively short) time, I'm soon on friendly or at least cordial terms with them again. But I haven't forgiven them- I never forgive anyone. Nor do I forget what they have done.
That, of course, includes myself (in fact I'm one of the people I find it hardest not to dwell on the wrongdoings of).
I suppose forgiveness is letting an emotional state you experienced vanish, disperse, disappear, to let it go. I understand entirely that that is a fulfilling, positive experience for many people. It is not, however, something I do- or indeed, I believe, am capable of doing. For me there can never be forgiveness.
Despite all I've written here, sometimes I think I'd like to forgive. At least, if someone were to actually turn to me and sincerely say "sorry", I would feel a certain weight lift. Whether this is similiar to "I forgive you", I'm not sure. I do know that on rare occasions hearing a "I forgive you" can move me very much.