The question of the Rishonim regarding the law of the stubborn and rebellious son is well known:
 

The Mishna in Sanhedrin 71b says: "The stubborn and rebellious son is sentenced in anticipation of his end. Let him die while he is innocent, and not die guilty."
 

The Baraitha in the Gemara elaborates on the explanation of the law of the stubborn and rebellious son: "It says in the Baraitha: Rabbi Yossi HaGalili says: "Since he ate a tartimar (between 213 and 240 grams) of meat and drank half a log (between 175 and 300 cc) of Italian wine, he is sentenced to death by stoning? The Torah foresees the end of the stubborn and rebellious son: that he will deplete his father's money and will desire the food and wine he is accustomed to and will not be able to procure them, and he will go out to the crossroads and rob the passersby. The Torah said: He should die while he is innocent and not die guilty."

The difficulty we have understanding the sentencing of the stubborn and rebellious son is first of all an emotional difficulty. How is it possible for the Torah to direct us to put a 13 year old boy to death? Beyond that is a halachic difficulty: how can one be punished because of his probable future? Every person has the possibility of doing teshuva.
 

In addition, the Chizkuni and the Re'em call attention to the contradiction from the story of Ishmael. When the water in Hagar's pouch was depleted, and she despaired of saving her son Ishmael, the angel of HaShem said to her: "…do not fear, as the Lord has heard the voice of the lad where he is … and the Lord opened her eyes and she saw a well of water, and she went to fill the pouch with water and gave the lad to drink." (Bereshis 21)
 

Rashi quotes Rosh HaShana 16b: the ministering angels said before HaShem: "Master of the universe! He whose offspring will kill Your sons with thirst, You are bringing up a well for him?! HaShem answered: what is he now - righteous or wicked? They said: righteous. HaShem said to them: I judge him by his deeds at the present. And this is (the meaning of) where he is."
 

And this is the difficult question: what is the difference between the stubborn and rebellious son, who is judged according to his end, and Ishmael who is not judged according to his end, but "where he is?"

There are many explanations among the commentators, and it seems that they can all be explained according to one fundamental point.

1. In the case of the stubborn and rebellious son, the process which will ultimately condemn him has already begun.

The Chizkuni and the Re'em explained that the stubborn and rebellious son already began the process of corruption which will lead him, in the future, to commit crimes which will make him liable for the death penalty: he doesn't listen to his parents, he is a "glutton and a drunkard" (Chazal interpret that he stole money from his father in order to buy meat and wine). In the case of Ishmael this process has not yet begun.
 

(On the other hand, the question arises: the Torah says in Bereshis 21:9 "And Sarah saw the son of Hagar the Egyptian, who she bore to Avraham, mocking." Rashi writes that the word metzachek – mocking – also implies idolatry, adultery and bloodshed. If so, didn't Ishmael also began to sin? I heard an explanation that the difference is that Ishmael didn't actually begin to commit the crime which was attributed to him (killing B'nei Israel by thirst), as opposed to the stubborn and rebellious son, who is judged upon the inevitability that he will plunder people, as he already began to steal money from his father and mother).

1. The difference between two kinds of "Beit Din"

The Maharal and other Acharonim explained that "that which is said, that a man is not judged except for his deeds at that hour" refers to the Heavenly Court, as one should not be judged except according to the present. But the worldly Beit Din judges him according to his end, in order to rescue him from the judgment of the Heavenly Court, which will judge him afterwards. In other words: the worldly court convicts and executes him in order that he will not die unpunished and therefore depart from this world without atonement.

1. The difference between the person himself and his progeny

The Maharsha explains on Rosh Hashana 16b: "The stubborn and rebellious son is judged on his own end, as opposed to Ishmael who is not judged on the future actions of his sons.
      

       4.  The difference between Israel and the nations

Only regarding Israel is it said that one is judged according to his end.

        5.  The stubborn and rebellious son came from "a woman of beautiful appearance"

The Ben Yehoyada (Rosh HaShana 16b) writes, in accordance to Rashi (Devarim 21:11) that the stubborn and rebellious son was born to an eishet yifat to'ar (a beautiful non-Jewish woman who was taken captive in war) and this son is min b'she'aino mino (a union of contradictory elements – a Jewish man and a non-Jewish woman) and therefore the law regarding him is different. 
 

         6. Ishmael repented

The Panim Yafot explains: "And I don't see a contradiction, as 'he should die innocent' is not relevant regarding Ishmael, since in the end he repented, as Rashi explains at the end of Parshat Lech Lecha (15:15): 'You will be buried at a good old age' – Ishmael will repent.
 

Evidently all of the disparities between Ishmael and the stubborn and rebellious son are different facets of the same explanation:
 

Apparently the sentence of the stubborn and rebellious son is not intended to punish him, but to absolve him. Even though it is possible that the stubborn and rebellious son will repent, in the final analysis this is extremely doubtful, and therefore we put him to death. And therefore the Mishna and the Baraitha explain "The Torah said: let him die while he is innocent, and not die guilty since the death of the wicked is beneficial to them and beneficial to the world."
Therefore: certainly HaShem's Divine Wisdom decreed that a person is not punished because of his end. However, the Torah has mercy upon its HaShem's creations, and in extreme cases - and there are sages who say that a stubborn and rebellious son who fulfills all the halachic criteria for execution has never existed and never will exist - death is preferable to life.
And so, for Ishmael, who is destined to repent, there is no benefit in being put to death.
But for a stubborn and rebellious son - who himself will sin and not his sons - it is a merit to die innocent.
And specifically regarding a stubborn and rebellious son who has already begun the process, and therefore will inevitably continue to deteriorate, we decree that it is a merit for him to die.
Additionally, the stubborn and rebellious son originates from an eishet yifat to'ar, so the chances that he will repent are even slimmer.
And specifically the worldly Beit Din acts in the manner of zakin l'adam (benefitting a person) and coercion to perform the mitzvot, which the Heavenly Court does not do, but rather judges the man and does not intervene with his choices.  
And it has more motivation to act to benefit a Jew than a goy.
 

Nevertheless, in light of this, a question remains: why does the Beit Din sentence the stubborn and rebellious son to the severe death of stoning? Tzarich iyun – we still have much more to reflect upon and learn on this subject…

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