what this means "so that's why sasuke..." and is that black figure kurama ?
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He means that Sasuke knew how much he cared for naruto and he felt he needed to kill naruto to kill what he believed to be a weakness, but naruto proved to sasuke that it is not a weakness to love another person and want to protect, hang with, and just do things with, like kurama realized once he realized naruto was not trying to control him or did he ever think of him as a monster.
That figure is Yang Kurama it's a flashback...of when Naruto was talking to Yang Kurama about wanting to remove all the hatred he had for humans.
Unless you know that Naruto talked to Yin Kurama like that and that would be moot seeing as it's the good part of Kurama and there is no hatred to begin with lol...
I'll help clear this up. Naruto had yang Kurama, because minato took the yin kurama for himself, up until when obito sealed yin kurama into naruto to save his life.
Here's one scan to prove yang kurama was originally inside naruto, not yin.
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Now as to how could he have those memories? It's possible because he is linked to his other half, learns when he learned when they came into contact and such.