G-d is described as being the One who pardons all our iniquities and is slow to chide and swift to bless (as in the yud gimmel middot).
Our mission in this world is to strive to emulate Him. Being godly and having a godly soul mandates that we be like G-d in our actions and dealings with all people. Since G-d’s forgiveness and love are without limit and have the potential to radically transform lives in ways beyond our comprehension, in emulating Him, we are duty bound to forgive. Without offering forgiveness to others, we are living lives that do not witness to and reflect G-d’s nature.