I'm not sure why AC don't have the same rivalry with Juve as Inter do
But traditionally Inter v Juve was always the biggest game.
Maybe it's dates back to the time that AC went 40-50 years without winning a title in the early to mid 20th century and Inter and Juventus were more regular winners
Taken from an article several years ago, quite interesting story actually
The animosity between Inter and Juve is by no means a recent thing, the two most successful clubs in Italy have a long history of rivalry – at least some 50 years of it, though no one knows for definite what started it, most think that the rivalry goes back to the 1960/1 campaign and the famous 9-1 Juventus win. The story goes that second-place Inter came to Turin in April of 1961 to take on first place Juventus.
Inter were only four points behind and had already beaten Juve 3-1 earlier that season in Milan. Unfortunately, so many fans turned up for the game (far more than the stadium could hold), that about 5,000 fans spilled out of the stands to watch the game from the sidelines, some even making their way onto the Inter bench.
Despite this, the game started as planned but half an hour into the first half, the referee ordered the game abandoned because of the Juventus supporters on the pitch. According to the rules, Inter was awarded a 2-0 win (Juventus was a awarded a win under similar circumstances a couple years previous to this ruling).
In typical Juventus style they appealed the decision to the FIGC (Funny how they didn’t appeal when the decision went their way!) and on the last day of the season, just before kickoff of the last game, the court ruled that Inter’s win would be repealed and the game would have to be replayed. In the eyes of Inter supporters and players, this ruling virtually handed Juve the championship.
To make matters worse, the head of the FIGC at the time was (no surprises here) Umberto Agnelli, the president of Juventus (and father of the current club chairman, Andrea Agnelli). Inter president Angelo Moratti (father of the current president, Massimo Moratti) and coach Helenio Herrera decided that they would field Inter’s youth team for that replay in protest.
Inter would play the game but it would be shown for the farce they felt it to be. The outcome was the 9-1 destruction of Inter by Juve and the birth of a rivalry that continues to this day. It is a bit staggering to think that events that occurred 50 years ago are still coloring how people view this game today but fans have long memories and the legend of that game lives on.