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.
The relationship between Naruto and Tsunade could be strained. Other villagers might notice the tension, and it could affect the overall morale of the village. Some might side with Naruto, thinking Tsunade is being too harsh, while others might understand Tsunade's pain and disappointment.
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 that Sakura betrays Naruto's trust. For example, if Naruto entrusts Sakura with a very important secret, like something related to his family or his new power he's developing, and Sakura reveals it to their enemies or uses it against Naruto in some way, that would be a huge blow to Naruto and could lead to him crying.
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.
One reason could be extreme emotional pain. Maybe he witnesses the death of a very close friend or loved one in the fanfiction world. This overwhelming grief could cause such a physical manifestation as crying blood.
One possible reason could be a misunderstanding. Maybe Naruto overheard some false information about Jiraiya and Tsunade that made him think they had wronged him or someone he cared about. For example, if he heard they were involved in a plot that led to the death of a fellow villager, it could turn his feelings sour.
Perhaps Naruto blames them for some of the hardships he faced. Maybe he thinks that Jiraiya wasn't around enough when he needed a mentor, and Tsunade didn't do enough to support him in certain situations. This could lead to feelings of resentment and hatred in the context of the fanfiction.
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.