The “speck” or “mote” refers to a particle of saw dust; the “beam” or “plank” refers to a large piece of lumber. A comparison Jesus would have been intimately familiar with being a carpenter and all.
In A Practical Commentry on Holy Scripture by Most Rev. Frederick Justus Knecht, D.D., published in 1923 and reprinted by TAN Books and Publishers in 2003, on pages 480-481, it says in part:
And why seest thou the mote[2] that is in thy brother’s eye, and seest not the beam[3] that is in thy own eye…
[2] The mote. The very smallest faults of your neighbour.
[3] The beam. The great faults which you yourself commit.
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*Censoriousness and detraction. *He who desires to find fault with others, must make sure that he himself is better than they! And yet, do we not constantly find that those men who have great faults of their own, are the very ones who judge the small faults of their neighbours most severely, not at all remembering their own short-comings? Such men are hypocrites, for they pretend to detest and avoid sin in others, while all the time they are loving and cherishing it in themselves. Furthermore, they sin against brotherly love by preferring to talk about what is bad in their neighbours, rather than about what is good in them, and they are more zealous in exposing their faults than in concealing them.
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*Venial sin and mortal sin. *By the distinction which our Lord draws between “motes” and “beams”, He teaches us that there is a great difference between one kind of sin and another.
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APPLICATION. Do not our Lord’s words about the mote and the beam smite your own conscience? You know the faults of others much better than you know your own, and you judge them severely, while you excuse yourself. The Saints did just the contrary: they were severe to themselves, and indulgent to others. Guard against uncharitable judgments and conversations.