A few people have mentioned that they thought Itachi could easily kill Pein using Tsukuyomi, since Pein sees everything from 6 different points of view. I think it's also plausible that Itachi can't kill Pein easily because Pein sees from 6 POV's.

I mean, think back to when Jiraiya taught Naruto how to break out of genjutsu. Jiraiya explained that genjutsu rely on manipulating the victim's brain chakra to create illusions. And Pein has 6 brains that seem to work together, using perfect telepathic team work. My "theory" is that Pein's telepathic vision technique is just genjutsu too. His eyes grant his bodies the power to transmit illusions to the other bodies by manipulating their brain chakra. And thinking back to Jiraiya's lesson on genjutsu, it can be broken by forcing chakra through your brain.

All this taken together makes me think Itachi can't kill Pein, at least not using the Rinnegan as a weakness.

Let's consider a scenario for examples. Suppose one of Pein's bodies (call it A) gets caught in Tsukuyomi. Then it means Itachi's chakra is messing with A's brain. Fine. But it doesn't mean Itachi knows how to force A to send the other bodies the illusion Tsukuyomi produces. Also, it is plausible that since the other bodies use genjutsu to maintain their link with A -- and thus they obviously know how to force chakra through A's brain -- that the others might just focus their chakra on A's brain and overpower Tsukuyomi.