According to the Bible, Absalom's conspiracy against David was motivated by his desire for power and revenge. Absalom's resentment towards his father began when David's eldest son Amnon, who was also Absalom's half-brother, raped their sister Tamar. David did not punish Amnon, which made Absalom feel angry and betrayed. Absalom plotted to avenge his sister's honor and killed Amnon two years later. However, David did not punish Absalom for this act, which further fueled Absalom's anger and ambition.
Absalom began to create a rebellion against David, winning the support of the people by portraying himself as a just ruler who cared about their grievances, while portraying David as an ineffective and distant leader. He gradually built up a powerful force, including the support of influential figures such as Ahithophel, one of David's advisors.
The rebellion reached its climax when Absalom entered Jerusalem and declared himself king. David was forced to flee, and a civil war broke out. However, despite having a larger army, Absalom was defeated by David's forces in a battle in the forest of Ephraim, and he was killed by Joab, one of David's commanders, against David's explicit orders to spare his son.
In summary, Absalom's conspiracy against David was driven by his desire for revenge and his ambition to become king. The resentment towards David began with the rape of Tamar and David's failure to punish Amnon, but was fueled by David's inaction against Absalom's act of vengeance, and Absalom's belief that he could do a better job of ruling than his father.