The season of heightened teshuvah is before us. The daily sounding of the shofar in the month of Elul , the early morning selichos, Rosh Hashanah, the Ten days of Penitence, culminated by Yom Kippur, the Day of Forgiveness. It is of interest that Yom Kippur is generally translated as the "Day of Atonement" rather than "Day of Forgiveness," although the term kapara generally refers to forgiveness. It is unknown who coined the term "Day of Atonement," but perhaps there is something to be learned from it.
In contrast to forgiveness, atonement connotes making restitution and compensation. This concept is not really relevant to sins of bein adam lamakom, between man and Hashem, because we cause Hashem no harm when we sin, as Elihu said, "Were you to have transgressed, how would you have affected Him, and if your rebellions were numerous, what would you have done to Him?" (Iyov 35:6). Chanun hamarbeh lisloach, Hashem’s mercy is infinite and HH His forgiveness is abundant, but that is only for sins between man and Hashem. If one has sinned against another person, Hashem does not forgive those sins until one has appeased whomever one offended. The Chasam Sofer said, "I am worried much more about sins bein adam lachavero than bein adam lamakom. I trust Hashem’s forgiveness, but I cannot be sure about people."
So for there to be forgiveness on Yom Kippur, there must be atonement, restitution, and that is not always easy to achieve. Ironically, easiest of all is if you were a goniff (thief) and stole something, because then all that is required is that you make monetary compensation. It is much more difficult if you maligned someone by speaking disparagingly of him. Here you may be in a quandary, because if you were to ask the person to forgive you for having spoken badly about him, you may cause him to agonize, "I wonder what he said about me and to whom." Rabbi Yisrael of Salant said that in this case it is better not to tell the person that you spoke badly about him, hence there is no way to ask for forgiveness. In addition, if you spread a false rumor about him, halacha does not require that he forgive you.
Whereas one can make restitution by returning the money one stole, there is no way of making restitution if you "stole" someone’s time. I.e., if you promised to meet someone at a certain time and you kept him waiting for twenty minutes, you deprived him of time, a commodity which cannot be replaced.
Perhaps you mistreated your child with improper discipline. You might have come from work having had a very difficult day and were very irritable, and were unjustly harsh to your child. That is an offense against another person which requires that person’s forgiveness. However, inasmuch as a child is legally incompetent, he cannot grant forgiveness, and Yom Kippur cannot erase that sin!
Bein adam lachavero applies to husbands and wives vis-à-vis one another. An abusive spouse incurs a sin when one mistreats one’s partner, and the aggrieved spouse may not forgive wholeheartedly.
Suppose someone asked your advice, and you told him what you thought would be best, but it turned out that your advice was misguided, and the person sustained a loss because of your advice. Although your intentions were good, you did inadvertently cause him damage, for which you are just as responsible as if you accidentally broke his window. The Steipler Gaon, in the very last moments of his life, cried bitterly, saying "I am afraid that perhaps I may have given someone bad advice."
What can we do about those situations where restitution is not feasible? One of the students of the Vilna Gaon felt that he had offended someone by sarcastically rejecting the latter’s explanation of a difficult Talmudic passage. He went from shul to shul throughout Vilna, looking for the man to ask his forgiveness, but did not find him and he was heartbroken. The Gaon told him, "If you have truly done everything within your power to ask his forgiveness, you can be sure that Hashem will put it in his heart to forgive you."
That is the solution for those incidents where one cannot atone. If one makes serious effort to make restitution and appease the offended people, then Hashem will put it in their hearts to forgive one. But one must be thorough in making restitution and asking forgiveness wherever possible, and that includes your spouse and your children if you have offended them, because only then will one merit Hashem’s intervention on one’s behalf.