Well this is selective reading, why do you only take Sais word on relieving Naruto of his burden and not his as well as Kakashis word on her wanting to go after Sasuke alone? The Sasuke thing was selfish in that she (mostly importantly) ignored Narutos feelings on the issue because of her own feelings for Sasuke.
You doubted Sai's words about being it for Naruto. Sai never said it's for Sasuke. He said it's for Naruto's sake.
Could you please explain this then?
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Fairly simple. But no one took the time to even think about it.
Let's go back a bit... What does Sai knows exactly about Sasuke's and Sakura's relationship to one another? Nothing.
So, you might wonder, why he said that? Well, let's remember one thing back in this time. Naruto said to Sai that Sakura loved Sasuke (but why? Sakura-chan loves Sasuke so much?! -> or something like that), so based on that, Sai came to the conclusion that based on Naruto's statement (Sakura loves Sasuke) and some personal beliefs (Sasuke sinking into darkness, which he witnessed himself, as well as wanting to save him in her own way, thing that he also knows for himself as he witnessed how Sakura and Naruto are trying to save Sasuke), Sakura's motive was the presented one.
But the "because she loves him" idea came from Naruto, as Sai doesn't know that, he hasn't seen Sakura's interaction with Sasuke, only Sakura's interaction with Naruto.
Hope you understood what I meant.