"And why beholdest thou the mote that is in thy brother’s eye, but considerest not the beam that is in thine own eye? Or how wilt thou say to thy brother: Let me pull the mote out of thine eye—and behold, a beam is in thine own eye? Thou hypocrite, first cast the beam out of thine own eye; and then shalt thou see clearly to cast the mote out of thy brother’s eye."
The defect in judging is the position from which we proceed. We are blind. We have too many subjective problems in our background. Our training, education, culture, presumptions, prejudices, "things we just know to be true", ignorance, preoccupations and impatience interfere with our perceptions. We act on errors and reach wrong conclusions. We measure with defective tools, then decide the matter from the wrong measure.
Christ is reminding us that whenever we are inclined to correct another person, more often than not, we suffer from whatever defect we see in others. This is why we notice it. We see it because it is really us. We are sensitive to the problem because we own the problem.
First, whenever we see something amiss in another, start with the realization that we are seeing ourselves. Start inside. Ask, "why does this bother me?" "Am I really seeing myself in a mirror?" Then be grateful you saw another person display your problem. You now know what is wrong with you. Forgive them, fix you.
The tendency to withhold patience is more often than not because their "mote" excites your notice through your own "beam." A "mote" is a speck, a bit of sawdust. A "beam" is a board. Yours is the greater defect. For in you is not only the defect, but the tendency to judge others harshly. Both are wrong.
When you have at last purged the defect, struggled to overcome and conquer the temptation or tendency, perhaps the price you pay to do so will make you humble enough to assist another. Not from the position as judge and condemner, but from the position of one who can help. When you "see clearly," then you may be able to "cast the mote out of thy brother's eye." For now you see him as your "brother." And in a kindly and affectionate manner you may act to reclaim him. Not as a judge, but as a brother.
This is a continuing petition to make things better. But the only way you make them better by starting inside. It is not for you to work on others, nor move outside your own range of defects, until you have first fixed what you lack. When you can proceed with charity to assist others to overcome what you have overcome yourself, then it is appropriate to approach your "brother" in kindness to help. Until then, stop judging and start removing "beams" from yourself.
Brilliant and peaceful. Revolutionary and kind. Christ is the ultimate True Teacher. He could teach such things because He was such things. His disciples will, in turn, take His teachings and His example and do likewise.