Jesus' message is a pretty simple one, although we can glean a deeper lesson from it by paying attention to every word in his message. In modern parlance, Jesus' message could be paraphrased, loosely, as follows:
Get your own act together before criticizing someone else.
A mote is a speck of dust. A beam is a log or a piece of lumber used in constructing ceilings and roofs. The former is almost infinitesimally small, whereas the latter is gargantuan. The humor in Jesus' comparison becomes readily apparent in the contrast between the two.
Put differently, Jesus is saying,
"After addressing and dealing with your own hang-ups and besetting sins you'll be in a better, humbler position to confront a brother about his hang-ups and sins."
One of the often overlooked terms in Jesus' teaching in this passage is the word hypocrite (see v.5). A hypocrite is a person who pretends to be something he isn't. Put differently, a hypocrite is someone who does not practice what he preaches. For such a person to confront and criticize someone else before taking stock of his own failures and sins is analogous to "casting the first stone" (see John 8:7).
After making a "searching and fearless moral inventory of ourselves," we are less likely to be so judgmental of others. Why? Because after conducting that inventory of ourselves we can see more clearly that
We are just as guilty and condemned before God as they are, whether they or we have committed one sin or a million sins. "All have sinned and fallen short . . ." (Romans 3:23). Sin entangles all of us, without exception (see Hebrews 12:1), and James reminds us that "we all stumble in many ways" (3:1, my emphasis). To forget this is the height of hypocrisy.
Our quickness to point the finger of blame at someone else can belie the presence of the very same (or similar) sin we are accusing our brother of. Again, this is hypocrisy.
Our tendency to detect a fault in a brother violates an important principle in Scripture; namely, "love covers a multitude of sins" (1 Peter 4:8; Proverbs 10:12 and 17:9). To cover a sin is not the same as to cover up a sin and pretend it never happened. No, God is our example in this. He does not cover up our sins, but he does cover our sins through the blood of the sacrifice of his Son, our Lord Jesus, who died for our sins (1 Peter 3:18).
There is a better way to confront someone caught in a sin. Paul summed it up in Galatians chapter 6:
"Brethren, even if anyone is caught in any trespass, you who are spiritual, restore such a one in a spirit of gentleness, each one looking to yourself, so that you too will not be tempted. Bear one another's burdens, and thereby fulfill the law of Christ" (vv.1,2).
In conclusion, there is a need within every local assembly of Christians to confront known sin. As Paul points out, however, only one who is spiritual is to do the confronting. Even then, spiritual people need to proceed with caution, because they are just as susceptible to stumble as the person they are confronting.
Rather than leading with a holier-than-thou attitude, they are to lead with caution and an I'm-just-a-sinner-too attitude. Sin breaks the heart of God, and sin should break our hearts, too, whether it is in us or in someone else.