One possible reason could be political pressure. Maybe some powerful clans in the village see Naruto as a threat due to his growing power and influence. They might force Tsunade's hand to banish him to maintain their own status quo in the village.
It could also be a misunderstanding. Perhaps there was a false accusation against Naruto, like he was framed for a crime he didn't commit. Tsunade, without having all the facts, might banish him in a hasty decision to maintain peace and order in the village.
In fanfiction, it could be due to a prophecy. Suppose there was a prophecy that Naruto would bring great danger to the village in the future. Tsunade, despite her bond with Naruto, might believe in the prophecy and banish him to prevent the foreseen disaster. Also, it could be related to Naruto's power. If his power was growing too rapidly and becoming uncontrollable, Tsunade might banish him to protect the village from any potential harm his power could cause.
Naruto could also become angry. He might feel betrayed by Tsunade and the village. This anger could fuel his determination to prove his innocence or worth. He could set out on a journey to become even stronger, so that one day he could return and show everyone that they were wrong to banish him. He might also start to question his own beliefs and values, which have been centered around the village and its people.
He could become determined to prove his innocence. Naruto is not one to give up easily. If he was wrongly banished, he would set out on a journey to find evidence or the real culprit to clear his name and return to the village he loves.
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.
Perhaps Naruto was falsely accused of something really serious in the fanfiction. Like he was thought to be involved with the enemy in some way. Kushina, being in a position of power, had to banish him to maintain the order and trust within the village, even if she didn't truly believe he was guilty.
One possible reason could be fear. The villagers have always feared the Nine - Tails within Naruto. His family might banish him out of this same fear, not wanting to be associated with the potential danger he represents. Maybe they think that by banishing him, they can keep the village safe from the Nine - Tails' power getting out of control.
One possible reason could be that Tsunade makes a decision regarding the village that Naruto strongly disagrees with. For example, if she refuses to send help to a neighboring village in need, Naruto, with his strong sense of justice, might get angry. He's always been about protecting and helping others.
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.
One possible reason could be political. After the war, the villages might be restructuring and Naruto, with his great power, could be seen as a threat. Another reason might be related to the secrets he knows. Maybe some powerful figures don't want him to expose certain things. Also, his Jinchuuriki status could play a role. People might still be fearful of the power within him even after the war.
One reason could be a mission. Maybe he gets a top - secret mission that requires him to leave the village under Tsunade's leadership without her direct involvement. So he has to leave without much notice.