Itachi's Physical Exertion to control Amaretsu1. My claim is not a 100% full proof one, but neither is yours. We don't have specifics on how genjutsu works, but if my Jirayia vs Pain genjutsu argument isn't valid, how about Ichibi (I think is his name) capturing one of the paths in a genjutsu?
Also, I have one logic that I follow when sustaining my argument that he only caught 3 paths, because judging by how fast the other bodies got to Jirayia, it could have only happened after the genjutsu, because otherwise they would have been too close and would have been caught as well. I am not excluding summoning jutsu and that may be the only leak in my argument.
2. Sakura was more receptive to his movements than you insinuate. Yes, he would have died if not for Chyio, but a full health Sasori could be read by 2 non sharingan users. By definition, sharingan users can see faster movements.
I will agree with you that Chyio is FAST, but remember that she went for Kakashi with full intent to kill, yet he stopped he on time, even when we wasn't prepared. And Itachi is faster than Kakashi.
"His skills of anticipation can't possibly evade something as instantaneous as sound" - here my argument crusher here:
A veeeery weakened Itachi was able to intercept Kirin, a jutsu that uses lighting (obviously travels at the speed of light). A solid object (unless it's Goku) cannot travel at the speed of light (by logic) because its mass would be infinite. Therefore, the magnets cannot be faster than Kirin and Itachi at normal strength can react to it.
3. for you whole argument, all I can say is this: think how Itachi burned the whole surroundings when fighting against Sasuke. All 100 puppets wouldn't be able to escape for sure am I correct? So amaterasu is still a valuable weapon in his arsenal. I'm not expecting him to deliver his final blow via amaterasu, but surely he would decimate his opponent's numbers.
Check. Your move.
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Whilst i agree about Amaretsu's destructive capabilities, i need to establish a misconception. In the manga scan shown above, its shows that Itachi had to maintain extreme concentration to control the black flames in order to burn down the fast majority of the forest, i highly doubt he could simultaneously move and manipulate considering the physical exertion it takes him for each individual movement of his flames.
Sasori's 100 Puppet Army and how looming the amount really is
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Along with Sasori's looming army of 100 Puppets, yes 100 seperate puppets acting, if even as little as one were to get through Itachi's Amaretsu, then he would be in no shape to dodge it. Immediately after using a MS technique, the user is shown to be weary, dizzy and prone to being hit relatively easily. This weakness could be manipulated all through out the fight against Itachi.
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Alright, now let's move on to discuss some other points.