Kisame does not want any part of Itachi which is why he obeyed every single one of Itachi's requests even though they were friends.
Yes he obeyed Itachi's every order and seemed to acknowledge him as his superior, yet when we saw Kisame fight WITH samehada, we saw that he is practically invincible and emortal as long as that sword is on his side, becoming strong the stronger the opponent he fights and samehada completely regenrating even fatal injuries like having his insides blown off by version two lariat.
We also find out that samehada can absorb even bijuu chakra which is said to be expremely corrosive and we saw what happened to oro when he touched 4 tailed naruto. Every jutsu requires chakra and without the chakra, there is no jutsu, except for taijutsu, the question arises then, how does Itachi beat Kisame when jutsu are useless, how does his sasuno'o stop great shark technique that absorbs all chakra it comes into contact with to make itself stronger and bigger until it destroys its target, making it impossible to stop with any jutsu that requires chakra to use or maintain.
Considering all this it becomes clear that the only way for Itachi to beat Kisame is to use tsukiyomi, but even that is questionable, would it work with samehada constantly disrupting Kisame's chakra?
Another thing we learned from manga is that for a genjutsu to take effect, the users tranfers his chakra to the other individual's chakra network and uses it to manipulate the other, which is why a genjutsu can be stopped if a teammate channels their chakra into your system, if that is the case, if the user has to TRANSFER the chakra to you, shouldn't it be useless when the other person has a capacity and speed chakra eater attached to them who can just absorb the chakra before it reaches him or from inside his sytsem?
Kisame with samehada is one of the most OP characters in the manga, Kishi even had to use plot no jutsu by seperating him and samehada just so that Kisame became beatable.
I think you're underating the man yo, its just that though, we can't dispute kishi even if some of the explanations of jutsu and abilities of certain characters makes them OP, if he says he is weaker then we have to accept, no matter how illogical it is.
You're right, Kisame did act like he was weaker then Itachi and he did even directly imply that Itachi is stronger then him when he said he couldn't handle a sannin but Itachi should be able to do it. He also followed Itachi's orders.
But also remember, before Kisame died, there was a flashback that revealed a converstion between Itachi and 0kisame, where we see Kisame basically threaten Itachi and tells Itachi to watch out for him.
