Rav Ashi, the author of the Gemara found it important to include this mini-sugya in to the Mesechta. But why? Abaya's assumption that Shmuel's ruling (of squeezing fish for it's brine) was totally mistaken, as proven by Rav Dimi. Certainly Abaye was entitled to err, but why record it?

The Mishna in Avos (5.7) says that one of the signs of identifying a wise person is that he doesn't interrupt when his friend is speaking. Rav Dimi used the name of Hashem to show his firmness in disagreeing with Abaye. He controlled his desire to interrupt Abaye and to shout out: "You're wrong!", but he waited patiently for Abaye to finish, and only then did he firmly but kindly show that Abaye was wrong.

Rav Ashi included this story within the Gemara to teach us: If the holy Amoraim treated each other with respect, certainly common people must listen to their colleagues opinions and only afterwards to give comment, be it approval or constructive criticism.