It's not just Italy. The UK is also insane along with some cities in Spain. In the UK one of the rivalries supposedly goes back to the War of the Roses [1].
The way I describe EU football games to Americans is take the craziest student section at a US college football game and extrapolate that energy to the entire stadium.
[1] https://en.wikipedia.org/wiki/Leeds_United_F.C.–Manchester_U...