Some mild theorizing in the form of fanfiction, all from some time ago.
As far as Kisame knew, the rest of the Akatsuki had never given much thought to what set off the current of fear that Itachi sparked in Orochimaru. Maybe as far as they were concerned, the gain of Itachi made up for the loss of Orochimaru, and that was all they cared about.
But Kisame had time to think about the matter over the years he spend quietly attending Itachi on their travels. For a while he chased the matter around in his head, patiently swimming circles around it, always pushing it forward, never going backwards. Finally, he narrowed everything down to a single memory.
In this memory, Itachi stood at the entrance to the meeting cavern, his head inclined slightly as Orochimaru murmured a few sentences to him. Then he turned and spoke a reply before walking off, and Orochimaru stood in displeased silence for a long moment after that.
That was how it started.
After some thought, Kisame asked Itachi one day what the words between him and Orochimaru had been.
Itachi bowed his head slightly in a moment's silence. Then he said, "He said that no matter how powerful I was, someday I would die, and he would not. And I told him that he was wrong. There is more than one way to impose your mind on another body and soul."