“Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.” (Col 3:16)
How can the word of Christ dwell richly in us in all wisdom if we just sing Psalms? The Psalms are not a complete record of the Person and work of the Lord Jesus, not of the Gospel which He preached. When a guy gets married, he should not be pre-occupied with pictures of his wife, but should become acquainted with the complete person that he married.
Exclusive Psalmody is a direct contradiction of Col. 3:16, which commands our music to be rich in the word of Christ.