Before we can even consider “forgiveness” (which only philosophers ever 1. consider or 2. do), we have to understand why people get such pleasure and elation over another’s real, or imagined, wrongdoing. The lure of making these kinds of “joyful” judgments outweighs any real assessment of the opprobrium. As much as people are driven to have what they believe is right and/or moral confirmed, they are way more driven to say someone else is bad or has done some bad thing. It is so “Human, All So Human.”
As for “letting go of moral anger,” again, only a philosopher would attempt this, and very few at that would. Most people consider moral anger to be a treasure to be maintained and hoarded and bragged about.
Look, the psychological defect of our society is “non-responsibility” and all that results from that defect. No one is responsible for anything bad, it is always either the other guy, or some imagined determinism like “genetics” or “upbringing” or some result of the imagined guilt of the beholder. Forgiveness only exacerbates the non-responsibility problem.