Joab killed Abner, Absalom, and Amasa

[TonyChanYT]

Long before Absalom's rebellion, David made a special deal with Abner, commander of King Ish-bosheth's army in 2 Samuel 3:

21 Abner said to David, “Let me go at once, and I will gather all Israel to my lord the king, that they may make a covenant with you, and that you may rule over all that your heart desires.”
So David dismissed Abner, and he went in peace.

Contrary to David's plan, Joab killed Asahel in cold-blooded murder in 2 Samuel 3:

27 When Abner returned to Hebron, Joab pulled him aside into the gateway, as if to speak to him privately, and there Joab stabbed him in the stomach. So Abner died on account of the blood of Joab’s brother Asahel.

In this case, the Bible told us the reason: personal revenge. Asahel killed Joab's brother, so Joab killed him. There was a bonus in this killing: Joab eliminated a potential competitor. Like Joab, Asahel would have been a high-ranking commanding officer working for David. So he had two personal reasons to disobey David.

Joab was instrumental in helping Absalom regain the trust of his father King in 2 Samuel 14. Yet Joab and Absalom had a personal conflict:

29 Absalom sent for Joab in order to send him to the king, but Joab refused to come to him. So he sent a second time, but he refused to come. 30 Then he said to his servants, “Look, Joab’s field is next to mine, and he has barley there. Go and set it on fire.” So Absalom’s servants set the field on fire.

It is consistent with Joab's character that he bore a personal grudge against Absalom for damaging his property. Once again disobeying David, Joab killed Absalom in 2 Samuel 18:14. Then David demoted Joab a chapter later in 2 Samuel 19:

13 And say to Amasa, ‘Are you not my own flesh and blood? May God deal with me, be it ever so severely, if you are not the commander of my army for life in place of Joab.’

However, Amasa was a bit slow and not completely competent in this new post when David ordered him to pursue another rebel named Sheba son of Bikri in 2 Samuel 20. So David sent out a second order to Abishai who outranked Joab at the time, 2 Samuel 20:

6 David said to Abishai, “Now Sheba son of Bikri will do us more harm than Absalom did. Take your master’s men and pursue him, or he will find fortified cities and escape from us.” a 7So Joab’s men and the Kerethites and Pelethites and all the mighty warriors went out under the command of Abishai. They marched out from Jerusalem to pursue Sheba son of Bikri.

Joab's crafty personality showed up for the 3rd time in 2 Samuel 14:

8 While they were at the great rock in Gibeon, Amasa came to meet them. Joab was wearing his military tunic, and strapped over it at his waist was a belt with a dagger in its sheath. As he stepped forward, it dropped out of its sheath.
9Joab said to Amasa, “How are you, my brother?” Then Joab took Amasa by the beard with his right hand to kiss him. 10 Amasa was not on his guard against the dagger in Joab’s hand, and Joab plunged it into his belly, and his intestines spilled out on the ground. Without being stabbed again, Amasa died. Then Joab and his brother Abishai pursued Sheba son of Bikri.

Once again, Joab had eliminated a rival to his position.

How did David react this time?

He promoted him:

23 Joab was over Israel’s entire army; Benaiah son of Jehoiada was over the Kerethites and Pelethites;

There was a complex relationship between David and Joab. Joab got David's jobs done efficiently, including David's dirty jobs, like killing Absalom, which was satisfying for Joab and good for David's hold on the throne.