In fact, Kakashi and Itachi didn't have much interaction. Apart from a slight friendship when they were in ANBU, other statements such as "they knew each other since childhood" and "Itachi had a private friendship after his betrayal" are all pure nonsense. Of course, except for the seventy-two hours of teasing when he was dragged into Tsukuyomi and trained hard in the future. Oh no, it was teasing.
Conception: