In Bob Kauflin's book Worship Matters, he has a section on how to handle criticism. He's writing specifically with church leaders in mind (pastors, preachers, music directors, etc.) but his insight proves to be super beneficial for all Christians.
He shows that criticism provides Christians with an opportunity to glory in the cross of Christ. He makes the point that the main reason Christians resent criticism is because we fail to believe what God has said about us at the cross.
He explains what he means by quoting Alfred Poirier: "In light of God's judgment and justification of the sinner in the cross of Christ, we can begin to discover how to deal with any and all criticism. I can face any criticism man may lay against me. In other words, no one can criticize me more than the cross already has."
Reflecting on these words, Bob writes:
What a thought. The cross is a loud statement of our sin, unworthiness, and need. And in light of the cross, we can receive criticism graciously because God, who knows our wickedness better than anyone else, has fully forgiven and justified us. We will never be brought into condemnation (Romans 8:1)! So we can confidently pray with David, "Let a righteous man strike me - it is a kindness; let him rebuke me - it is oil for me head; let my head not refuse it" (Psalm 141:5).
Once again I was reminded that because I am in Christ, all that I need I already have-even the capacity to endure criticism with great gospel joy and thanksgiving.