Step back and see the whole passage as one unit. Jesus forbids the critical heart, warns that our measure returns to us, and then commands us to deal with our log so we can gently help our brother. But it ends in a problem we cannot solve. The man with the log is blind. How do you remove a beam from your own eye that you cannot even see? You cannot. You need someone to do it for you.
And that is the gospel. The King who arrived in Matthew 1, the one with all authority, did not stay on His throne and judge us from a distance with the measure we deserved. If He had used our own measuring cup on us, that measure would have condemned us. Instead the Judge of all the earth stepped off the bench, walked into the courtroom, and stood in the place of the guilty. He took the judgment we had coming. He was treated as the hypocrite so that we could be treated as sons and daughters. He took the log, He took the speck, He took all of it.
Dane Ortlund reminds us in Gentle and Lowly that Jesus deals gently, and only gently, with sinners who come to Him. The very gentleness we are so bad at giving, He gives us in full. Remember the Beatitudes: the kingdom first makes you someone who sees your own log and grieves it and brings it to Jesus. That is where radiant faith and gentle hands come from.
So if you belong to Christ, here is what is true of you: your measure has been poured out on Him, your log has been carried by Him, and you are dealt with gently. Now go and do likewise. Look in the mirror, let Him take the log out, and then with clear eyes and gentle hands go love your brothers and sisters enough to help them with their specks. That is the proof that your faith is real and not just talk.