1 John 1:9
If we confess our sins, he is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.

The forgiveness of our sins rests solely on the faithfulness of God.

When David was confronted with his sin, he appealed to the faithful loving-kindness of God. Having betrayed Uriah and corrupted Bathsheba, David knew that he could not appeal to his own faithfulness. He could not approach God on his own merit, for he had none.

This is why he claims to have sinned against God alone is Psalm 51. David was not unaware of how his actions had affected those caught in his web of deception, but he knew that absolution for sin comes from God alone.

God forgives those who confess their sin and turn to Him seeking forgiveness. David could only appeal to the faithfulness of God for cleansing from his sin, and it is no different for us. Only through the atoning sacrifice of Jesus Christ is forgiveness made possible, and only the Father can issue that forgiveness to us.