What does “a bruised reed He will not break” mean in Matthew 12:20?

Matthew 12:20 (quoting Isaiah) says of Christ:

"A bruised reed He will not break, And smoking flax He will not quench, Till He sends forth justice to victory;"

Reeds are used for making music as well as musical instruments. A broken reed cannot produce song so it is quite useless. Nobody bothers with a broken reed because reeds are as common as grass. You just discard and replace the ones that are defective. Man is the reed here. When you have no song or you've lost your song because of your sins and imperfections, Christ will never give up on you as man would. He will help and restore you to glory when you utterly depend on Him for salvation from your stain of imperfection aka sin.

It is no coincidence that Peter's given name was Simon. Christ changed His name from Simon (meaning “reed”) to Peter (meaning “rock.”) Peter's transformation was not immediate. After his name change, he continued to act like a reed: easily swayed by the elements. He sank from his unbelief as he walked on water. He denied Christ three times after knowing 100% that he could never do something like that. He even thought Christ was wrong when He told him about his then upcoming denials, just as many who think that some sins are beneath them do today. But Christ did not abandon him to wrath. Peter rested in God's Grace and the cowardly reed who denied Christ three times out of fear after boasting that he would not was transformed by the Holy Spirit to a bold rock/pillar of the church; filled with the Holy Spirit, Peter publicly preached a sermon where 3000 people got saved, this in full glare of the religious Jews who previously scared him and who were still out to kill the followers of Jesus.

No matter how fallen or broken you are because of your sins and imperfections, when your trust is utterly in Christ for Righteousness and Strength, He will not abandon you to wrath. He will save you from your brokenness and your sins. This is why He came- Matthew 1:21-

“She will bear a Son; and you shall call His name Jesus, for He will save His people from their sins.”

Trust in Him, putting no confidence in what you think you can do to mend yourself and He will transform you from a battered reed to a solid rock as He did Peter.

But what about a smoking flax? Many of us are familiar with a smoking flax or wick like the one in the second image below (images are from the Internet)

When forces/circumstances affect the fire of a lamp like that in the first image which was commonly used in the middle east, the fire dies out leaving a faint glow. A strong, choking and unpleasant smoke (sins and imperfection) begins to emanate from the wick/flax. Our natural reaction is to see the smouldering and smoking wick as useless and harmful. We snuff it out completely to stop the smoke from choking us. We cast it aside and look for a good one that is suitable for our needs. But not Christ. A smoking flax He will not quench. Notice that a smoking flax can do absolutely nothing to help itself. When all you can produce is your choking and unpleasant smoke of sins and imperfections and you trust utterly in Christ to restore you to life, He will supply you with His oil (anointing) and restore you to His shining glory that will give light to the world. Only believe, and this we do by Grace. Beloved of God, Grace is a Person. His name is Jesus Christ. Titus 2:11 says of Him:

"God’s marvelous grace has manifested in person, bringing salvation for everyone."

Verse 14 of the same Titus 2 says: "He gave His life to free us from every kind of sin, to cleanse us, and to make us His very own people, totally committed to doing good deeds."

With Christ, acknowledging our disqualification (utter imperfection) and consenting to be saved by Him are the qualifications required for His salvation. The one who thinks he can achieve anything good by himself or thinks that his human effort-driven attempts at attaining godliness (be like God) count for something does not see his utter need for the salvation of Christ who knows us inside out and sees that by default, the heart of man is desperately wicked. Just like Peter before he denied Christ, those who think they are or can be righteous by themselves (the self-righteous) are yet to see that they are only standing because of God's mercy that has kept them from the vagaries of Time and Chance and has not allowed Satan to sift them like wheat. Only in the righteousness and strength of Christ do we get to stand, have life and have it more abundantly. In Him, God sees us as righteous, even though we are bruised and smoking; even though we are guilty of many sins- Romans 5:16-

"And the result of God’s gracious gift is very different from the result of that one man’s sin. For Adam’s sin led to condemnation, but God’s free gift leads to our being made right with God, even though we are guilty of many sins.”

God's abundance of Grace and His gift of Righteousness to us in Christ is not so that we should continue to wallow in sins as antichrist pastors love to imply and as it seems to man's natural reasoning. In Christ, we never remain as a bruised reed or a smoking flax. The word of God whose ways and thoughts are higher than man's says receiving His abundance of Grace and His gift of Righteousness to us in Christ is the Way to live in triumph over sin and death. See Romans 5:16-17:

"And the result of God’s gracious gift is very different from the result of that one man’s sin. For Adam’s sin led to condemnation, but God’s free gift leads to our being made right with God, even though we are guilty of many sins. 17 For the sin of this one man, Adam, caused death to rule over many. But even greater is God’s wonderful grace and His gift of righteousness, for all who receive it will live in triumph over sin and death through this one Man, Jesus Christ."

This is right believing. Believe Right and you will Live Right.