Fr. Robert Barron had an excellent reflection a year ago, on the tenth anniversary of 9/11, on righteous anger, charity, forgiveness, and redemption:
He strongly makes the point here that the main difference between righteous anger and sinful anger is its connection with charity. Anger at injustice, that compels more strongly the willing of the good of the other, is righteous anger, of the sort (as he points out) that the Bible ascribes to God. But anger at injustice that clings to the harm done leads rather to some sort of vengeance, than to forgiveness.
One of the further things this distinction entails is a purification of memory. As we know from our experience, we retain the memory of sin, both as sinner and as sinned-against, even after sacramental confession. These memories can be powerful, and can affect our charity, often for ill. It's very easy, in fact, to cling to the memory of the harm done, and to allow that memory to tempt us back into sin. Often, when the sin is our own, we move from the memory back into the same sin, seeking even despite our (struggling) will and (incomplete) desire for God the fleeting sweetness of sin's illicit pleasure.
But it's also too often true, when we have been harmed by sin, that, as we remember the harm done, we are tempted against charity to desire a comparable harm to the one who harmed us (or, perhaps, to a substitute "them"). In short, as Fr. Barron says, we desire vengeance, not justice. Vengeance is so much easier than justice, both because vengeance doesn't require me also to change, the way justice does; and also because vengeance contains that same illicit sweetness of sin.
I believe this is in fact extremely common. Most of the time, it leads us to petty and instant vengeance, like yelling at a child who's disobeyed or dropped their dinner on the floor, or like cursing the driver who's just cut us off. Most of the time, we recognize both that further acts of vengeance would be themselves a completely unjust escalation of the original harm, and that we don't truly desire that kind of harm to the other. Clearly, this is good, in the sense that we are resisting the temptation to greater sin, even if we are giving in to the temptation to the lesser sin.
But that's precisely the issue, for those who belong to Jesus Christ. If we thus justify at a personal level the lesser sin of "verbal vengeance," we cultivate the habit of anger separated from justice and charity, and we put ourselves in a very poor spiritual position. We reflect very poorly the beatitude of meekness (the absence of anger, if not from our reaction to injustice, as we've seen, then at least from our motive in responding). Socially, we slowly escalate the level of "verbal vengeance" that is acceptable, and therefore that is necessary to portray. The more socially necessary it is to speak violently, the more abused and dominated are those who cannot do so (convincingly). At some point, this tips from verbal to physical actions, and the cycle of domination continues apace. This aptly describes our culture, in fact, and represents a key measure of the marginalization of our Christian heritage.
Thus, as followers of Christ, we need to practice a purification of our memory. This can be part of our regular examination of conscience. If we cultivate in the memory of the daily, petty harms inflicted on us the habit of letting righteous anger move to charity, rather than to self-serving vengeance, then we might be capable of the same in remember the more significant harms. Likewise, when we are the ones harming, if we cultivate a desire to seek forgiveness and redemption in the memory of the little things, we might be able to do so in the more significant.