Perhaps Tsunade was under some sort of mind - control or influenced by a dark power. This power could have distorted her perception of Naruto and made her act against him in ways that were harmful.
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.
It could be due to a misunderstanding. Perhaps there is false information circulating about Naruto that Tsunade believes. Like if someone spreads rumors that Naruto is involved in some dark plot, Tsunade, in her role as Hokage, might take hasty actions against him. Later, when she realizes it's all a lie, she regrets it.
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 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.
One possible reason could be to search for a powerful artifact. In many fanfictions, there are often hidden and powerful items that can change the fate of a village or even the whole ninja world. Naruto and Tsunade might leave Konoha to find such an item before their enemies do. This would be a dangerous mission, so they keep it a secret from the rest of the village to avoid panic.
It could also be related to personal relationships. Tsunade might have been hard on Naruto in a way that he felt was unjust. Perhaps she was overly critical of his unorthodox ninja techniques or his impulsive nature, and over time, this built up into hatred. Naruto, being someone who values respect and recognition, could have resented her for not seeing his potential in the way he wanted.
The story could develop with other characters getting involved. For example, Sasuke might hear about what happened and come back to the village to confront Tsunade. This would create a lot of tension and drama in the fanfiction.
One possible reason could be a misunderstanding. Maybe Tsunade misinterprets Jiraiya's actions or words. For example, if Jiraiya writes something in his book that Tsunade takes the wrong way, she might lash out at him. Another reason could be related to their past. If there are unresolved issues from their earlier days together, like an old argument or a failed mission where they had differences in opinion, it could lead to Tsunade hurting Jiraiya in the fanfiction. It could also be a situation where Tsunade is trying to protect Jiraiya in a strange way. She might think that by pushing him away or causing him physical or emotional pain, she is actually saving him from a greater danger that she foresees.
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.
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.
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.