This is just my basic opening argument.
Following post will include scans, DB pages, and links
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Kankurou is a puppet master of the hidden Sand villiage. He's commonly known for his trickery and ver strategic approach in battle. While I admit I'm at the disadvantage here, Kank has the ability to open up victory against Itachi.
Due to Itachi bein sick, he almost always avoids using MS unless absolutely necceaary. This makes it highly unlikely that Susano'O will come out due to its massive chakra drain and Itachi not having reserves to spare. Itachi prefers to fight in base to and without MS to limit chakra drain. He mainly focuses on Taijutsu and Genutsu due to there minimal chakra drainage. Here lies Kankuro's chance a victory.
Kankurou, being a puppet user a avoids direct combat. He can keep his distance with a multitude of puppets and with his knowledge he can deduce that he shouldn't look into Itachi's eyes from the fax that he has knowledge of Sasuke Uchiha and the far that the Uchiha were talented in Genjutsu. This is aided by the fact that he doesn't fight directly, minimizing chances of eye contact.
Puppets will also be hard to deal with, Genjutsu being non effective against them and being dosed in poison makes them ideal for combat against Itachi. Will Itachi fends of one if the puppets, crow can use poison gas to catch Itachi off guard and poison Itachi. Mix that with his sickness and Itachi's body will begin to fail him. Itachi will also have a hard time fighting multiple puppets at once that all have fatal attacks from poison.
Kankurou will also keep at least one puppet near him, given that Itachi has shown to use MS lightly in his battles, there is a chance of Amaterasu. Kankurou can use this puppet as a fail safe against Amaterasu. Given Itachi's chakra reserves he wouldn't risk using it more than once.
Itachi's Fire style can be countered by the Sasori puppets flamethrower.
When Itachi finally decides that he will need to use Susano'O, Kankurou will be well prepared and have a puppet laced ndergrond ready to capture Itachi (like sai's brother).
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This is a real down and dirty argument since I'm on an iPod and can't refine it ATM.