Theophylact of Ohrid

But these words are applicable to all, and especially to teachers, who while they punish the least sins of those who are put under them, leave their own unpunished. Wherefore the Lord calls them hypocrites, because to this end judge they the sins of others, that they themselves might seem just. Hence it follows, Thou hypocrite, first cast the beam out of thine own eye, &c.

Catena Aurea by Aquinas ↗

Bede

And how can you say to your brother: Brother, let me cast out the speck from your eye, when you yourself do not see the beam in your own eye? You do this with your brother if (for example), what he sins by anger, you criticize by hatred. And just as a beam is to a speck, so is hatred to anger. For hatred is anger long-standing, which with the passage of time has so grown that it is rightly called a beam. It can happen that if you are angry with a man, you wish him to be corrected. …

On the Gospel of Luke ↗

Bonaventure

Second, he shows that such a one is indiscreet in speech, because he does not speak reasonably; on account of which he adds: Or how can you say to your brother, namely, by addressing him outwardly: Brother, let me cast out the speck from your eye, in reproving and correcting; while you yourself do not see the beam in your own eye? not attending to the most grievous sin in yourself, as if to say: you cannot reasonably say this. For it could be said to you: Why do you judge another, and do not judge yourself? …

Commentary on Luke, Chapter 6 ↗