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This psalm's superscription attributes it to David. It is a part of God's Word, and therefore it was written under the inspiration of God. We have to conclude that God, under certain circumstances, permits a flawed human the right to hate. If it is all right for a flawed human to hate under certain circumstances, then it is certainly all right for the perfect Creator God to do so.
As "hate" is used here, we should not conclude that God is speaking of a virulent and malignant passion that desires to destroy the life of another. The words "loathe" or "grieved," as modern translations use, defines and limits the hatred to deep sorrow for or strong disapproval of the conduct of those under discussion. David did not desire to be associated with them; he wished to avoid their company and find his friendships among those of beliefs and conduct like his. Conclusion? God does not love everybody equally, nor does He expect us to. Psalm 5:5 concurs: "The boastful shall not stand in Your sight; You hate all workers of iniquity."
John W. Ritenbaugh
The Sovereignty of God: Part Three