IIRC, each of the two Argentinian Navy battle groups, led by the Belgrano and their aircraft carrier Veinticinco de Mayo respectively, had one of our hunter-killer submarines tagging along. The one with the Veinticinco de Mayo couldn't get a clear shot (due to fog?) otherwise it would have been sunk first as it was the greatest threat. And so it was the Belgrano that was attacked.
Sinking a big ship like the Belgrano made a huge impact (no pun intended) both politically and militarily. When the Belgrano went down, the Argentinian leadership realised they had no answer to our submarines and that we could also sink their real pride and joy the Veinticinco de Mayo, which together with the rest of their Navy promptly retreated to Argentinian territorial waters and stayed there for the rest of the conflict.