The ancient city of Hebron was a good place for Absalom to start his rebellion. It is first mentioned in Genesis 13:18, when Abraham lived there and worshipped Yahweh there. David lived there and was even crowned king there, first over Judah and then over all Israel (2 Sam. 2:4; 5:3). Absalom himself had been born there, and given the fact that he started his rebellion there, it is likely that he had kept up with his contacts there through the years.
It is also very likely that at least some of the people of Hebron were unhappy with the fact that once David became king over all Israel he moved his capital city to Jerusalem. After all, Hebron was a city in the tribal area of Judah, and David was a Judean from Bethlehem. Furthermore, it was the Judeans who supported David in his rebellion against the house of Saul the Benjamite and anointed him king over Judah. Thus it is very likely they felt that David was ungrateful and had abandoned them when he moved his capital city from Hebron to Jerusalem, a city in the tribal area of Benjamin. Between Hebron’s ancient roots as a city of Yahweh, Absalom’s contacts in Hebron, and a likely dissatisfaction among some of the Hebronites with David, the city of Hebron was the perfect place for Absalom to start a rebellion, and Absalom’s rebellion almost succeeded.