It is not "forgive and forget" as if nothing wrong had ever happened, but "forgive and go forward," building on the mistakes of the past and the energy generated by reconciliation to create a new future.
A stiff apology is a second insult... The injured party does not want to be compensated because he has been wronged; he wants to be healed because he has been hurt.
Sometimes we can take offense so easily. On other occasions we are too stubborn to accept a sincere apology. Who will subordinate ego, pride, and hurt-then step forward with 'I am truly sorry! Let's be as we once were: friends. Let's not pass to future generations the grievances, the anger of our time'? Let's remove any hidden wedges that can do nothing but destroy.