“he was very angry.” The Septuagint adds to the text, and some English versions add the Septuagint addition to their English text. For example, the NRSV adds: “but he would not punish his son Amnon, because he loved him, for he was his firstborn.” Other English versions that add the Septuagint ending to the text include the BBE, CEB, Douay-Rheims, NAB, and NJB. The addition, while no doubt partly right in the reason why David did not deal with Amnon, was not likely in the original Hebrew text but was likely an explanatory note added in the Greek text. Most scholars have concluded that the original is preserved in the Hebrew text.
David was very angry but did nothing. Likely for many reasons. No doubt David’s own adultery played a part, as did the fact that Amnon was his firstborn son. However, one of David’s faults was his indulgent affection for his sons (but not for his daughters), something that shows up several times in the biblical narrative, and it shows up here. Sadly, David was like many parents who do not raise their children in both the “training” and “admonition” of the Lord (Eph. 6:4). David did not upset his children by reproving and correcting them (1 Kings 1:6), but reproof and correction, and putting up with the emotional pain that children feel when they are reproved, is a necessary part of good parenting.
David apparently had a totally different relationship with his daughters than he did with his sons. While David indulged his sons and was blind to their faults, even coming close to losing his own life due to his blindness, there is no indication that he felt the same way towards his daughters. This was in part cultural, for example, David’s sons are listed in Chronicles but only his daughter Tamar, and that almost certainly only because of the part she played in the eventual death of Amnon. Nevertheless, that daughters would be treated so differently from sons was certainly not God’s intention or what we tend to think about a “man after God’s own heart.” There is no indication in the text that David sought any kind of justice for Tamar, or even did anything to comfort her. In fact, not only are no other daughters of David named in the Bible, even Tamar is never called David’s daughter, only the sister of her brothers, David’s sons.