Why does "Mizmor" apply to Avshalom's rebellion? It should say Kinah (lamentation)!
Rashi and Radak, citing Brachos 7b: David said this "v'Ma'ale ha'Zeisim Oleh u'Vocheh" (Shmuel II, 15:30). Why did he say Mizmor amidst crying? Since the Navi told him "I will establish against you evil from your house" (Shmuel II, 12:11), David feared lest it be a slave or Mamzer, who would not have mercy on me. Once he knew that it is his son, he rejoiced.
Rashi citing a Midrash: David saw that his entourage endured; his slaves, and the Kereisi u'Pleisi, i.e. the Sanhedrin, considered him their master. He said "let us flee from Avshalom", they said "whatever my master, the king, will choose, behold your slaves [will obey]" (Shmuel II, 15:14-15). When he came to Machanayim, Shuvi ben Nachash, Machir ben Ami'el and Barzilai ha'Gil'adi came to greet him and financed him (Shmuel II, 17:7).
Radak citing Shocher Tov: David said, Yakov fled - "va'Yivrach Yakov Sedei Aram" (Hoshe'a 12:13). Moshe fled (Shemos 2:15). I flee like them! I thought that I was Chayav Misah. Now that I am exiled, exile atones (Brachos 56a)! "Zacharti Mishpatecha me'Olam Hashem va'Esnecham" (below, 119:52) - I remembered the earlier ones, and You conducted with me like You conducted with them. I was consoled, and I knew that via fleeing, my sin was pardoned.
Radak: They were not called Mizmorim at the time [that David composed them,] rather, because they were Memzamer (sang) them in the Mikdash. The same applies to "b'Vo Do'eg ha'Edomi va'Yaged l'Sha'ul" (52:2), "b'Vo ha'Zifim" (54:2) and "va'Yishemru Es ha'Bayis Lahamiso" (59:1). Similarly, those said on the exile and the Churban of Yerushalayim, like "Mizmor l'Asaf Elokim Ba'u Goyim b'Nachalasecha" (79a) and all said about David at the time he was in danger - after he was saved from all of them, they were Mizmorim and praise and thanks to Hashem. Those said about the exile were Mizmorim when the exiles returned 1 .
Sha'arei Teshuvah (4:12, from Shocher Tov 79): Tzadikim pay their debt, and sing to Hashem. A parable for this is a sharecropper who owed his employer. The employer took the entire harvest, and the sharecropper left empty, and he was happy - the document is finished. I paid my debt!
Presumably, David saw so with Ru'ach ha'Kodesh and called them Mizmorim. It is difficult to say that later Chachamim changed [even slightly] the text of Tehilim! (PF)
Why is this Mizmor after the previous one?
Radak: [Mizmor 2 discusses when] Pelishtim came against David to contest his kingship and fight him. Also Avshalom his son thought to take the kingship from his father and kill him. David defeated all of them and remained king.
Radak citing Brachos 10a: [Mizmor 2 discusses] Gog and Magog. If one will ask, does a slave rebel against his Master 1 , say to him, does a son rebel against his father?! Rather, it happened - also [Gog and Magog] will occur.
Many rebelled against Hashem! Keren Orah (Sotah 10a) - it was incredulous that one would rebel against Him after the honor of Shamayim's kingship will be revealed to everyone.
