Christ desires to forgive rather than condemn
When the woman caught in the act of adultery was brought before Jesus by the Pharisees and the Scribes, they were not seeking legal advice from Jesus, they were setting a trap. If Jesus authorised capital punishment then He could be reported to the Romans – the Jews were not permitted to administer capital punishment. If Jesus forbade the stoning, He could be discredited as a false messiah because He contradicted the Law of Moses, which made adultery a capital offence (Lev 20:10; Dt 22:22).
So Jesus’ response is a way of thwarting their trap: “He who is without sin cast the first stone.” He neither authorises the stoning, nor does He forbid it. The genius of His response is of course that He turns the tables on the Pharisees. They have now been trapped in their own snare. Although the Pharisees might well have regarded themselves as sinless (as Saul had done, see Phil 3:5-6) they knew that if they had condemned the woman to stoning the power of Rome would have fallen on them. So the Pharisees walk away because they are frightened, and thus they have been made to look like sinners, which they didn’t believe was true, but Jesus knew was true!
The Pharisees’ actions are a warning for those who are tempted to condemn others and bring the full weight of the consequences on that person. They also warn us that we need to be more sensitive to our own sin (which we can truly do something about) than other’s sin. The Lord is merciful and so must we be. However we must be under no illusion that adultery (and all the sexual sins that come under that heading) is a grave sin. Jesus does not condemn the woman, but neither does He condone her sin. She is forgiven rather than condemned. By the action of Christ, by grace, she is made ready to be able not to sin again, which is what Jesus exhorts her to do.
This mercy of Christ to desire forgiveness rather than condemnation is what He offers us all in the Sacrament of Penance. Our imagination tells us sometimes that confession is condemnation, but that is a lie. Our Lord is merciful and so the Church’s Sacrament dispenses Christ’s mercy to all of us who are sinners and who are repentant. Let us repent and receive that mercy as often as we can, that we may have the grace to sin no more.