Does the ability to forgive require sin?

If a person comes to another person and asks for forgiveness but does not identify the sin is it truly possible to forgive them? Another way to ask: Does forgiveness require a sin?

If a person says they are sorry for someone “feeling hurt” but no sin is present is forgiven even possible? Is saying I am sorry for some action I did, although not intrinsically sinful, but it did hurt the other persons feelings does that need to be forgiven or is it possible to forgive this?

Example: In a group discussion I talk about the differences between a Catholic and Protestant view of how Jesus’ atonement is applied to our lives. A person is offended and hurt by me explaining these differences. My explanation of these differences is not sinful but if I say I am sorry that I hurt this person is that a sin that needs to be forgiven? Even though I didn’t break any of God’s moral, natural, or eternal laws?

If there was no sin, what would they be forgiven of? Could God be forgiven? What would that even mean?

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