בַּיּ֤וֹם הַשְּׁמִינִי֙ שִׁלַּ֣ח אֶת־הָעָ֔ם וַֽיְבָרֲכ֖וּ אֶת־הַמֶּ֑לֶךְ וַיֵּלְכ֣וּ לְאָהֳלֵיהֶ֗ם שְׂמֵחִים֙ וְט֣וֹבֵי לֵ֔ב עַ֣ל כָּל־הַטּוֹבָ֗ה אֲשֶׁ֨ר עָשָׂ֤ה יְהוָה֙ לְדָוִ֣ד עַבְדּ֔וֹ וּלְיִשְׂרָאֵ֖ל עַמּֽוֹ׃
On the eighth day he sent the people away, and they blessed the king, and went unto their tents joyful and glad of heart for all the goodness that the LORD had shown unto David His servant, and to Israel His people.
Akeidat Yitzchak
The reason that sins committed between different human beings are not subject to atonement of Yom Kippur is, that any sin in which man's body is the major party, can only be atoned for by that same body making the appropriate restitution. When reconciling oneself with one's fellow man, it is the senior person, the scholar, who must make the first move, just as Abraham had done with his nephew Lot. (Genesis chapter 13)