We read in the Haftorah this week, "And Adonijah Ben Haggith rose up and said, I will be king" [Kings I 1:5]. At first glance, Adonijah had all the proper credentials to take over the kingdom. He was the fifth son of David, after Avshalom, who was fourth, so that from the point of view of age he took precedence over Solomon. He also showed that he understood the niceties of pomp and circumstance, as was fitting for a king: "He made for himself chariots and horsemen, and fifty men who ran before him" [ibid]. He also had a very impressive appearance: "He was very handsome" [1:6].
However, Adonijah lacked the lessons of parental authority. "And his father had never stopped him to ask, why did you do this?" [ibid]. The fear that an educational comment by a father might put the son in a bad mood and might interfere with his ability to serve G-d with joy kept Adonijah from learning one of the basic tenets of education: authority. And for this reason he lacked the ability to give commands, which is the main factor in government and authority.
This lack is hinted at in his name. It starts with the first three letters of G-d's name, aleph-dalet-nun, and ends with the first three letters of another name of G-d, heh-vav-yud-heh. He is missing the fourth letter of this name, which is related in the Kabbalah to the "sphere" of Malchut - sovereignty.
The ability to reign is based on an assumption all desire for sectorial divisions will be abandoned. However, Adonijah is not wise enough to form a link with all the sections of the nation, and he distributes benefits only to those who hold opinions close to his own. "And Adonijah sacrificed sheep and cattle and fatted bulls at the Even-Hazochelet near Ein Rogel, and he called all his brothers, the sons of the King and all the men of Judah, the servants of the King. But he did not call Nathan the Prophet and Benaiah and the warriors, and his brother Solomon." [1:9-10]. The fact that he included Abiathar, the rejected priest, at his table shows an extra measure of conservatism and a refusal to recognize the improved priesthood practiced by Tzadok. And calling on Joab Ben Tzruya was an attempt to preserve the old style of military leadership, which by rights should have been replaced by Benaiah, who would combine Torah and the army.
Perhaps the memory of the events surrounding Bat-Sheva deterred David from showing open support for her son Solomon. Or perhaps he felt that the dynasty should not be fathered by one who entered his home as a result of a moment of weakness. But then the association between Bat-Sheva, who reminded him of his sin, and Nathan the Prophet, who chastised David harshly for taking Bat-Sheva, showed David that Solomon was indeed worthy of becoming King. He was brought to the realization that the dynasty must include within it elements of sin that were forgiven, in order to enhance the understanding of human urges among the leadership of the nation. No leader can empathize with the soul of the nation, which has its ups and downs, if he has never come into direct contact with failure, at least from the point of view of his family roots.