It could also be due to a broken spirit. Naruto might have faced a series of devastating events, such as the loss of many friends in a short period or the destruction of the village he loves. He may have lost all hope and see death as the only way out of his pain.
One possible reason could be extreme guilt. Maybe Naruto has done something he believes is unforgivable, like accidentally causing the death of a beloved friend while in a fight. He might think that death is the only way to atone for his mistake.
One possible reason could be that Naruto feels he has become a threat to the village or his friends in some way. Maybe he has some sort of dark power within him that he can't control and he believes Sasuke is the only one strong enough to stop him. Another reason might be related to a prophecy or a greater threat that Naruto thinks his death can prevent, and he trusts Sasuke to carry out this difficult task.
Naruto might be longing for a motherly figure in his life. He has always been alone and has seen how others have mothers. Tsunade, being a strong and caring woman in the village, could be someone he looks up to and wishes to have as a mother.
Perhaps he has been through some sort of mental and emotional breakdown. Maybe he has lost too many battles, seen too many friends die, and he feels that he is a burden or that his death would somehow bring peace to his troubled mind. It could also be related to some prophecy or dark secret he has discovered about himself that makes him think death is the best option for everyone.
It might also be due to a sense of hopelessness. If he's faced with an enemy that seems truly unbeatable and he fears the destruction of the village or his friends, he could ask to be killed to prevent further harm. For example, if there's a powerful villain who has Naruto's friends hostage and the only way to save them is by Naruto sacrificing himself.
One reason could be extreme despair. Maybe he has faced so many hardships and losses that he feels there's no way out. For example, if he has lost many friends in battles against powerful foes and he blames the gods for not protecting them better.
Tsunade would probably be shocked at first. Naruto is like family to her. She might immediately refuse and try to talk some sense into him. She could say something like 'Naruto, you're stronger than this. There's always a solution to every problem.'
Maybe Naruto discovers some dark secret about Tsunade's past that she has been trying to hide. For example, something related to her lost loved ones. Naruto, in his usual straightforward way, confronts Tsunade about it without realizing how much it would hurt her, and thus makes her cry.
Well, Harry may have realized that Sirius is his godfather, which means there's a special bond already. He might think that living with Sirius would give him a proper family environment, filled with love and understanding, unlike what he has at the Dursleys' place. Also, Sirius has a rebellious and free - spirited nature that Harry might be attracted to. He could hope to grow up in a more exciting and accepting atmosphere.
One possible reason could be a misunderstanding. Maybe Tsunade received some false information about Naruto that made her think he was a threat to the village, so she took actions that ended up hurting him.
She might be initially shocked. Given her own past traumas and her relationship with Naruto, she could be hesitant at first. But then, considering Naruto's lonely situation, she might warm up to the idea and show a more maternal side towards him.