In this chapter, Absalom overthrows his father and David flees for his life.
This chapter begins with Absalom amassing power and prestige for himself. He almost immediately demonstrates that he is more interested in his own honor and glory than the glory of the LORD, so it is unlikely that he would reign the way that God wishes.
The second thing worth mentioning is how Absalom's rebellion against David is contrary to how David himself treated Saul. When Saul was king, he attempted to kill David to protect his own throne and legacy. Now that David is king, it is his own son and likely heir to the throne that is remarkably attempting to overthrow his own father. Absalom essentially betrays David the same way that Saul (incorrectly) thought that David was going to betray him. In particular, David says "I will not lay a hand on the LORD's anointed"; Absalom shows no such reservation.
The third thing I'd like to point out is the peculiarity of Absalom's rebellion itself. Amnon, David's firstborn, is dead. Absalom slew him. Kileab is David's second-born, and he is only mentioned once in the entire bible. Although ostensibly he is now David's heir to the throne, some commentators suggest that he must have died in his youth to explain why Kileab is never mentioned in relation to the various rebellions against David or the eventual succession of Solomon.
If that were the case, then Absalom would be next in line for David's throne. However, it's possible that David disowned him after he murdered his brother. It's not exactly clear if that's the case after "the king kissed Absalom" in the previous chapter. By the ordinary pattern of inheritance, Absalom should be next in line for the throne. It would only be if David has disowned him that the throne would fall to one of Absalom's brothers, and that is the only situation where Absalom's rebellion makes any sense. It would be totally insane to try to usurp your father's throne if it's falling to you after he dies anyway. It's the equivalent of trying to steal from yourself. So I think it's more likely that David has already told Absalom that he would not be king, and Absalom is acting to secure his own future over the kingdom.
This chapter repeats the pattern from the previous couple chapters, which is David's weakness and undeserved trust for the people around him; in this case, Absalom. Absalom is amassing chariots and servants and through his good looks and charm, "stealing away the hearts of the men of Israel", and David does nothing about it. I wonder if David even realizes that his son is taking the kingdom out from under him. Absalom again asks David for permission, this time to depart to another city and David allows him to do so. David is blindly trusting, even though Absalom is trying to build his own power base. All I can imagine is that David doesn't realize Absalom is preparing a coup despite how public that behavior is. I mean, Absalom is literally standing at the gate talking to people as they enter the town about how he should be a judge, and David doesn't realize what is going on. This is unfortunate naivety on David's part, and it will cost him.
Absalom begins his rebellion by going to Hebron, which is interesting because Hebron was previously David's royal city and one of his most significant power centers, because it is (in a vague sense) like a capital for Judah, which is David's tribe. So Absalom's decision to go there reveals that David is losing the loyalty not just of the others tribes, but even his own tribe. One commentary I read suggested that Hebron turned against David because David moved the royal city from there to Jerusalem, which is an interesting suggestion.
The first decisive action David takes is to flee from Jerusalem, and it possibly saves his life. He was slow to realize Absalom turning the hearts of the people against him (by claiming that there was nobody with the king who could give them justice) but once he realized what happened, it seemed like the old David kicked back into life. Ironically, this is the second time David has had to flee for his life from the royal city; last time he was fleeing as a servant of Saul, and this time he is fleeing from his own throne which is about to be taken from him.
The rest of this chapter is essentially a parade of David's supporters, listing all of the prominent figures and groups that travel with him into exile or support him in other ways. All of these groups and individuals will remain deeply influential after Absalom's revolt is quashed, as this event is one of the first filters applied to see which of David's men are true to him and which are only interested in power and wealth.
David himself has spent many years wandering and running for his life, but many of the prominent figures in his kingdom joined him after he became king, so for many of them this is a decisive moment. David had no choice when he was sent into exile, but David's men do have a choice: Absalom would likely accept just about anyone who would swear loyalty to him. That makes the decision of those who go with David all the more significant.
It begins with the "mighty men", the Pelethites and Kerethites, and alongside this group it also mentions 600 Gittites, which is a demonym for the people of Gath. That these three groups are listed together suggests they fill a similar role, as loyal troops and enforcers of David's regime. The Gittites are most interesting because they are definitely not Israelites, so it is possible they are converts to Judaism. They also show exceptional loyalty, seeking to go with David into exile.
Next it lists Zadok and the Levites. It should not surprise us to learn that the religious authorities side with David given the prominence that David has placed on the ark and the temple and other things of the LORD. David has been a fervent (and by all accounts sincere) promoter of the LORD as king over Israel, which politically benefits the priests and Levites whose livelihood is dependent on how many sacrifices the people offer to the LORD.
As David goes past the Kidron valley and up the Mount of Olives, the story concludes with a tale of two counselors. The first counselor, Ahithophel, deliberately betrays David and goes to serve Absalom. The second counselor, Hushai, remains loyal to David and tries to go with him into exile.
I think these three groups also represent the different seasons and situations in David's life. He built the loyalty of the Pelethites and Gittites when he was in exile in Gath and the Negev, proving himself to be a rugged man and a fighter. He built the loyalty of the priests and Levites during the early days of his kingship when he brought the ark back to Jerusalem and tried to build a temple (though he was eventually dissuaded). The two counselors represent the political and administrative aspects of his kingship, as he increasingly drifts away from his shepherd youth and fugitive adolescence and is now becoming much more of an old, staid authority figure and managing complex international politics as Israel claims dominance over some of its neighbors and fights wars against others.
Out of these three groups, only the first one is permitted to go with him. David commands the priests, the ark and Hushai to return to Jerusalem and serve him by spying out Absalom's plans and to thwart him from within as a fifth column. It should not surprise us much that the two groups who supported him during his reign as king would be least capable of toughing it out in the Judean wilderness, and therefore he sends them back. They mean well, but it's unlikely they have the skills or endurance to help David in these kinds of situations, while the Pelethites and Kerethites cut their teeth being hunted by Saul alongside David.