No, he ordered him to take him with them, and that was a weakened Kakashi.
They pulled back when Guy arrived as well.
Itachi never admitted Jiraiya is above him.
And again, Itachi was on Konoha's side. He wasn't going to hand over the Jinchuriki of the most powerful tailed beast over to the Akatsuki. It's painfully clear that Itachi was aiding Konoha, and Jiraiya was the perfect excuse.
He said their titles pale in comparison, and named the Uchiha clan. Obviously an average Uchiha is not on Jiraiya's level, but Itachi is not an average Uchiha, and is beyond Jiraiya.
We don't even know if Kisame knows how Itachi beat Orochimaru.
Orochimaru literally says Itachi is stronger than him
That's what it looks like when a characters expresses inferiority to another character in strength. Not like what you imagined occurred with Jiraiya.
Let's make this really simple.
Since you somehow believe Jiraiya beats Itachi, and Itachi and Kisame (lol), does he also beat the entire Akatsuki? Itachi says that backup would be futile in the battle.