Have you ever wondered why Itachi was paired with Kisame, well it simple, Kisame was to kill Itachi if he ever showed a sing of disloyalty to the Akatsuki organisation, let me explain
Obito introduced Itachi to Akatsuki but he never really trusted the man. It was evident that Itachi killed his clan to save his village, which is sort of dangerous for someone who wanted to end the dominion of the 5 villages.
It was only fair to pair him with someone who has keen ears for the Truth and also who is a direct polar opposite of his Abilities, someone who Itachi can't catch off guard easily with his genjustu, and Kisame was the perfect pick.
Kisame was the polar opposite of Itachi's mangekyo Sharingan abilities, this is because Kisame is a Jinchuriki, a perfect Jinchuriki is a tailed beast that helps its owner eg killer Bee, and Naruto, Kisame although wasn't a Jinchuriki of a tailed beast he could defuse with Samehada, if Itachi was to put genjustu on Kisame and block his chakra flow, the Samehada could offer his chakra to kisame thus eliminating Itachi's genjustu.
Kisame is also a Chakra absorber so he can absorb the Amaterasu and Susanno Chakra if it was ever used against him by Itachi.
Lastly, the reason why they were both paired was that they were considered the strongest members of the Akatsuki after Nagato Pain, so it was only right to pair the two second strongest in the Akatsuki organization to watch each other's backs!
