Rico Tice comments well on this passage:
It upsets religious people enormously to hear this powerful and authoritative figure say, “I can heal you, but if you don’t think you need a cure, you can forget it. I’m here for the sick.” Jesus makes it clear that people who think they are good enough without him don’t want his help, just a healthy people don’t want doctors. That’s a problem for a lot of us. As Tom Ripley says in The Talented Mr. Ripley: “Whatever you do, however terrible, however hurtful, it all makes sense in your head, doesn’t it? You never meet anybody that thinks they’re a bad person.” But Jesus says here, “I’ve come for people who realize that they’re bad people, for those who know that they’re living as rebels in God’s world.” In other words, for sinners.
So, the qualification for coming to Jesus is not “Are you good enough?” but “Are you bad enough?” Jesus is categorically not interested in people who think they are good. He is devoted to those who realize that they are bad. (Taken from Christianity Explored, p. 21)
It is terribly refreshing to remember that Jesus does not just save sinners, but He only saves sinners. No one will benefit from the saving work of Jesus other than sinners. No one goes to heaven because they are a good person. The only people who populate heaven are those who confess they only deserve hell.
This has tremendous power for those struggling with guilt on account of their sins. Martin Luther give us a great example of this in when he shared this story: “Once, when I was racked with pain and sin, Satan said, ‘Luther, you can’t be saved, for you are a sinner! ‘No,’ said Martin Luther, ‘I will cut your head off with your own sword. You say I am a sinner; I thank you for it…because Christ died for sinners, therefore he died for me.”
For the bad people. Are you a sinner? Have you turned your back on God, ignored His Law, and worshiped something else? Have you spit in the face of grace and lived in glad rebellion? Have you committed more sins than you can remember? Take heart, a Savior has come looking to save folks just like you: sinners.
For the good people. You really aren’t good (and you know that) and thinking you are good disqualifies you from the saving work of Jesus Christ. You may not think that is a great problem because you don’t think you need Jesus. Rest assured, your comfort is an illusion and your danger real. You are a like cancer patient who refuses to see the doctor and be properly diagnosed and treated. You live like you don’t have cancer, but it, not you, will have the final word. The longer you think your healthy, the more dangerous it becomes for you.