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Itachi: - please dont look into my eyes just please dont do it........
That has no bearing on the fact that the Genjutsu was already cast, and that Bee broke out of it. That warning only applied to future Genjutsu attempts, not one that had already occurred.
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Then Naruto says dont look into his eyes cuz Tsukuyomi will kill ya. 1sec = 72hours, bee can break it faster than this. Fail son.
And Naruto fully understands the machinations of Tsukuyomi, of course, despite having never been cast in it nor possesses a Sharingan. Truly the best source of information on Genjutsu.
Fact of the matter is that any Genjutsu requires you to overwhelm the opponent's illusory defenses, and the only reason it worked so easily was because Part 1 Kakashi and a 5 year old Sasuke had pathetic illusory defenses compared to Itachi. That isn't the case here, with Obito.
Hebi Sasuke showed that Itachi cannot simply Tsukuyomi a competent target in 1 second and call it a day; he has to overwhelm the opposition's Genjutsu defenses, and will be rendered immobile, unable to capitalize on any openings until said illusory defenses have been defeated. The same is shown with Kakashi vs. Obito, where neither fighter moved until the Genjutsu was over.
You are under the impression that all Itachi has to do is cast Tsukuyomi. That is not the case; he must cast it and then engage in a Genjutsu power struggle with the target and pray to overwhelm their illusory resistance. That is far easier said than done against Obito.