Tigay (1996, p. 196) writes "the law seeks to deter filial insubordination, but by requiring that the case be judged by the elders, it also places limits on parental authority, as does the previous law." Similarly, Barry Eichler (2010, p. 451) writes, "the essential purpose of the Torah is to protect the child from the absolute and capricious authority of the father even as it seeks to strengthen parental authority by deterring filial insubordination." According to these scholars, the law has two goals, limiting the power of the parents, and deterring rebellious children, but these goals are contradictory. If the power of the parents is limited, then this encourages children to be more insubordinate. Furthermore, how is the power of the parents limited if they can have their son killed?
Eichler reviews several laws in ancient times to show "that patriarchal authority over one's wife and minor children was a potent force in ancient Near Eastern societies." We see this absolute power in the Torah by the story of Yosef. When the brothers of Yosef returned without Shimon and told Yaakov that they could only return to Egypt if they brought Binyamin with them, Reuven offered to kill his two sons if he did not bring Binyamin back to Yaakov (Bereshit 42:37). How could Reuven offer to kill his sons? What had they done to deserve to die? The answer is that it appears that in biblical times the parents had absolute power over their children and could kill their kids without even having to make any claims.
Accordingly, since Devarim 21:20 requires the parents to speak to the elders and to explain why they want to have their son killed, this law is a limitation on their powers. The elders do not appear to act as judges, but just the requirement to make a public declaration has the potential to stop the parents from acting capriciously. Furthermore, as noted by Tigay (p.197) the parents do not participate in the stoning, which means the parents must be convincing enough that the other people of the city are willing to stone their son.
This need to prove the parent's claim might be the reason why the parents have to also state that their son is a glutton and a drunkard. Other people cannot really determine if a son is listening to his parents, but they can observe him to see if he is a glutton and drunkard. The boy is not being killed for drinking and eating excessively, but this is the minimal proof that is needed to convince people to accept the parent's claim that their son is not listening to them. Relatively speaking this minimal proof was significant since in those days no proof was needed at all for parents to kill their sons for disobedience.
Therefore, the point of the law was only to limit the powers of the parents. Even though the Torah allows the parents to have their son killed, still in the context of the absolute power wielded by parents in ancient times, the law limits their powers in some ways. In addition, maybe there was only a need to limit the powers of parents in reference to disobedient sons and not daughters, if in those days daughters were not sufficiently independent to rebel to the extent that parents would want to kill them.
If the Torah was trying to reduce the power of parents over their children, why did the Torah not just abolish the power altogether? The answer to this question follows the Rambam's (Moreh 3:32, see also our discussions on Shemot 20:3 "Other gods," and Bemidbar 15:32-36 "Sticks and stones") explanation as to why the Torah commands people to offer sacrifice even though according to the Rambam, G-d does not really desire sacrifices, that the Rambam argues that in those days people could not conceive of a religion not having sacrifices. Similarly, in those days the culture was so ingrained that parents have absolute powers over their children that the most the Torah could do was to limit these powers.
This idea can explain the development of this law in the rabbinic period. While some opinions (Mishnah, Sanhedrin 8:5, R. Yose ha-Galili, Sanhedrin 72a, quoted in Rashi on 21:18) attempted to justify the killing of the son that it was better for him to die innocent than to be guilty of real crimes later on, other Rabbis effectively neutralized the law by adding numerous conditions that it could never happen. For example, R. Yehuda (Sanhedrin 71a) stated that the son can only be judged a disobedient son if the voice, looks and heights of both parents are equal. Why did the Rabbis add these conditions to abrogate the biblical law? The answer might be that they realized that the Torah was trying to limit the power of the parents, but could not completely end this practice due to the cultural background of the people. However, when the Rabbis realized that people were able to accept that parents do not have complete absolute power over their children, then they added these conditions to end this ability of parents to kill their children.