Why did Jesus respond like he did in the story of the woman caught in adultery (John 8:3-11)? Why doesn’t He respond like that in other situations?

The story of the woman caught in adultery goes like this: The teachers of the law and the Pharisees brought in a woman caught in adultery. They made her stand before the group and said to Jesus, “Teacher, this woman was caught in the act of adultery. In the Law Moses commanded us to stone such women. Now what do you say?” They were using this question as a trap, in order to have a basis for accusing him. But Jesus bent down and started to write on the ground with his finger. When they kept on questioning him, he straightened up and said to them, “If any one of you is without sin, let him be the first to throw a stone at her.” Again he stooped down and wrote on the ground. At this, those who heard began to go away one at a time, the older ones first, until only Jesus was left, with the woman still standing there. Jesus straightened up and asked her, “Woman, where are they? Has no one condemned you?” “No one, sir,” she said. “Then neither do I condemn you,” Jesus declared. “Go now and leave your life of sin”—John 8:3-11. This is an interesting story, in part because it does not appear that this particular story is in the original manuscripts. The translators of the King James Version would have found it in their manuscripts because their documents only went back about 600 years from their time. Obviously, the farther back into history you can go, the closer you get to the “original autographs,” in other words, the actual original writings of the authors of the New Testament. Now while we don’t have those, we have scrolls that have been dated back to the 4th century AD—six hundred years later than what the King James scholars had to work with—and this particular story is not found in those manuscripts; the older texts go directly from John 7:52 to John 8:12. A similar discovery is made in regard to the remainder of Mark chapter 16 after verse 8. This tells us that this story, as wonderful and inspiring as we may think it is, was added in a later edition of manuscripts. Now, this doesn’t mean that it didn’t really happen; it certainly may have. We simply don’t have the documentary attestation to back it up. But that being said, why did Jesus respond as He did? Several reasons come to mind: (1) Jesus understood that their question was being asked merely as a trap, as the text says, simply to “have a basis for accusing him.” That would not put them in a place where they were eager to learn a lesson. So, how to proceed? Let them teach the lesson to themselves. That is what’s going to happen if they honestly confront His question to them. That may make a clearer memory than anything He might say. (2) They brought a woman “caught in adultery.” Simple question: Where was the guy? Adultery’s really hard to do as a solo; it pretty much always needs a “partner in crime.” Again, the crowd was not particularly interested in either truth or justice, and Jesus saw clear through them. (3) Dealing with them as He did allowed the crowd to disperse, leaving Jesus free to have a brief, but hopefully life-changing one-on-one with this woman. Let’s not forget: She had sinned. Jesus even intimates at a “life of sin” and, for this woman to be willing to risk her life for such sinful behavior, it can be argued that she was a pretty hard-hearted character. But then she was confronted with Jesus. He clearly saved her physical life, and also allowed her an opportunity to come to a life that could save her for all eternity.
The story takes place in the climate of an interesting challenge—one that our modern sensibilities might not appreciate. Jesus is challenged with the situation of very obvious, open sin, and then reminded of Moses’ words—the Law. Now if Jesus’ opinion was contrary to the Law of Moses, His credibility as a rabbi worthy of notice would be shot, and the Law of Moses—given through Moses but given by God—was very specific in this instance: If a man commits adultery with another man’s wife—with the wife of his neighbor—both the adulterer and the adulteress must be put to death—God speaking, Leviticus 20:10. Moses reiterated this teaching in his benedictory in Deuteronomy: If a man is found sleeping with another man’s wife, both the man who slept with her and the woman must die. You must purge the evil from Israel—Deuteronomy 22:22. Pretty clear stuff, but if Jesus was in lockstep with Moses, He would appear to be a whole lot less compassionate and forgiving than His ministry had led people to believe. The point from the Pharisees’ point of view? Whatever it takes to discredit this Nazarene. Jesus’ response is perfect—of course—and totally disarms His enemies, partly because He refers them to their own Scriptures: If your very own brother, or your son or daughter, or the wife you love, or your closest friend secretly entices you, saying, “Let us go and worship other gods” (gods that neither you nor your fathers have known, gods of the peoples around you, whether near or far, from one end of the land to the other), do not yield to him or listen to him. Show him no pity. Do not spare him or shield him. You must certainly put him to death. Your hand must be the first in putting him to death, and then the hands of all the people—Deuteronomy 13:6-9. And the second scripture, also from Moses’ own words, paints very much the same picture: If a man or woman living among you in one of the towns the Lord gives you is found doing evil in the eyes of the Lord your God in violation of this covenant, and contrary to my command has worshiped other gods, bowing down to them or to the sun or the moon or the stars in the sky, and this has been brought to your attention, then you must investigate it thoroughly. If it is true and it has been proved that this detestable thing has been done in Israel, take the man or woman who has done this evil deed to your city gate and stone that person to death. On the testimony of two or three witnesses a man shall be put to death, but no one shall be put to death on the testimony of only one witness. The hands of the witnesses must be the first in putting him to death, and then the hands of all the people. You must purge the evil from among you—Deuteronomy 17:2-7. The point that Christ is making is simple, and yet devastating: If you are completely “not guilty” of this or any other sin, then declare that, in front of this woman and everybody else by throwing the first stone. Begin this process that you demand; kill her. If you’re perfect, that should be no problem. Right? Of course, Jesus would make a similar point during the Sermon on the Mount: Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you. Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye—Jesus Christ, the Sermon on the Mount, Matthew 7:1-5. And regarding the possibilities of our own righteousness, the epistle that James wrote pretty much put that idea to rest: For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it—James 2:10.
Jesus always responded as best fit the situation. Obviously not every situation was the same. A poor, uneducated person was going to get a different response than was a Pharisee, who lived a life of ample resources and intense education. One of the reasons that Jesus responded with such venom to the Pharisees in so many situations was because they had the truth of God’s intentions, and they manipulated that knowledge for their own benefit, whereas God wanted His word and His commandments to reach and change people’s lives for their eternal benefit.