“First Take the Log Out of Your Own Eye” by John Piper

One other saying of Jesus confirms how he designs mercy as a way of governing our experience of anger. One of the ways that anger expresses itself is in judging others. Jesus gave us a demand in this
regard:
"Judge not, that you be not judged. For with the judgment you pronounce you will be judged, and with the measure you use it will be measured to you. Why do you see the speck that is in your brother’s eye, but do not notice the log that is in your own eye? Or how can you say to your brother, “Let me take the speck out of your eye,” when there is the log in your own eye? You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother’s eye." (Matt. 7:1-5)
The command not to judge sounds as absolute as the command not to be angry. “Judge not, that you be not judged.” But what follows the command shows us that there is a kind of judging that is bad and a kind of judging that is necessary and good—just like there is good and bad anger. When Jesus says, First take the log out of your own eye, and then you will see clearly to take the speck out of your brother’s eye,” he shows that it is necessary to make judgments about the speck in a brother’s eye. What turns this kind, caring,healing judgment into the judgmentalism that Jesus forbids is the failure to see the log in our own eye. It is the same as the unforgiving servant failing to live in the awareness of the “log-debt” that he had been forgiven (ten thousand talents), so that he could gladly forgive the “speck-debt” of his brother (one hundred denarii). Jesus assumes that when we see the log in our own eye, we know how to remove it—that is, we know how to find forgiveness and help from Jesus. otherwise the delicate procedure of removing the speck from the eye of our brother would not be possible. You can’t do delicate, loving eye surgery with a log hanging out of your eye.
So the point of Jesus’ words about judging are to show us how the anger of judgmentalism can be broken. It is broken by a broken heart. We live in the consciousness of our own great sinfulness and in the awareness that only the mercy of Jesus can take the log out of our eye with forgiveness and healing. This awareness turns angry judgment into patient and loving forbearance and delicate correction. Legitimate anger may remain because we are displeased that eye-specks bedevil people we love. But that anger is not the anger of judgmentalism. Good anger is governed by the experience of mercy.
Excerpt from What Jesus Demands from the World by John Piper
Reformation Theology