David asked God to let all who take refuge in Him rejoice and shout for joy forever that God might spread a cover, a canopy, over them to cause those who love God's name to exult in God. He also asked God to bless the righteous man, surrounding him with favor as with a shield (Psa. 5:11-12). I do not know why David prayed all these things here. Instead, he should have prayed, "Lord, forgive me. My sinful conduct caused my son to rebel. Lord, have mercy upon him. Move us all to repent to You." There is no hint in these psalms of David being convicted of his sinfulness.
In God's chastisement, David asked God to be gracious to him, to heal him, return to him, and save him for the sake of His lovingkindness (Psa. 6:1-5). David realized that he was in God's chastisement, but there was still not much confession about his failure. He said that he was wearied with his groaning, causing his bed to swim all night long, dissolving his couch with his tears. His eye had wasted because of grief and had aged because of his enemies (vv. 6-7). I think that this is David's exaggeration. Can anyone cause his bed to swim by his tears? Do we agree with this kind of prayer? If a brother prayed this way in a prayer meeting, we might admonish him to stop this kind of prayer.
David believed that Jehovah had heard the sound of his weeping and that all his enemies would be ashamed and greatly dismayed (Psa. 6:8-10). David could not forget his enemies. This is different from the Lord's teaching in the New Testament.
David took refuge in God and asked God to deliver him from all who pursued him. The enemies, including his son, were chasing after him. David felt that he had done no wrong (Psa. 7:1-5). How can anyone tell God that they have done no wrong?