Chazal make it very clear that Yom Kippur atones only for sins that are בין אדם למקום, between man and G-d, and not sins that are בין אדם לחבירו, between man and man.
In order for us to truly clean our slate, we must ask forgiveness for people that we may have hurt in the past. We would not want others to be dwelling on the pain we may have caused them.
It is difficult for us to have to confess our wrongdoings to Hashem. But it may even be more difficult to have to say we are sorry to another individual.
Perhaps an even higher level would be to be able to forgive those who have wronged us and they did not ask us for forgiveness. Despite their bad behavior, if we can find it in our hearts to forgive them anyway, it brings us great merit.
Yom Kippur is meant to be a day of atonement and forgiveness for all of כלל ישראל.
And, if I insulted or hurt any of you in any way, please forgive me. גמר חתימה to all.