It could be due to jealousy. Some villagers might be jealous of Naruto's power and Hinata's noble status. So, they spread false rumors that lead to their banishment.
Hinata would develop more leadership qualities. With Naruto gone, she realizes that someone needs to step up and be a symbol of hope for those who still believe in Naruto. This would make her more confident in making decisions for the greater good of the village and its relationship with Naruto when he returns.
Perhaps there is a misunderstanding about Hinata's Byakugan abilities. It is thought that she and Naruto could use it in a dangerous way. This leads to their banishment. In their exile, they discover new powers within themselves that are not related to the Byakugan, which they then use to fight against the false accusations and return to the village.
A great fanfiction I remember has Naruto being banished unjustly. Hinata decides to go with him. Their relationship blossoms in exile. They learn to rely on each other more than ever. The story beautifully portrays Hinata's loyalty and Naruto's determination to protect his new family. It's a heart - warming tale that explores their characters in a different setting than the original series.
A great 'naruto x hinata banished' fanfiction is the one where Naruto is banished after being wrongly accused of a crime he didn't commit. Hinata, in a bold move, defies her family's wishes and goes with Naruto. In exile, they have to build a new life from scratch. This fic focuses a lot on their character development as they adapt to their new situation and how their relationship evolves from friendship to love.
In these fanfictions, a common theme is the exploration of the characters outside the constraints of the original Naruto universe. Naruto's banishment frees him from some of the duties and expectations in the Hidden Leaf. Hinata also gets to break free from some of the traditional Hyuga family limitations. Their marriage then becomes a symbol of their new - found freedom and a journey of self - discovery as they face the world together.
These fanfictions exist because many fans like to explore alternative storylines. The idea of Naruto being banished adds a lot of drama and conflict to the story. Hinata's relationship with Naruto in these scenarios allows for a deeper exploration of her character, especially her loyalty and love for Naruto.
In this fanfiction, Hinata could be badass in a way that she challenges the village elders directly about Naruto's banishment. She argues that Naruto has been the savior of the village multiple times and his banishment is unjust. As she does this, she also showcases her new and improved combat skills, which she has been secretly honing, to intimidate those who oppose her and show that she will fight for Naruto's return.
Naruto might also initially feel a sense of abandonment. However, his kind - hearted nature could lead him to try and see the good in the situation. He could start to explore the world outside, learning about different cultures and ninja techniques. He may use this experience to become more empathetic towards others who have also faced hardships, and in the long run, this banishment could be a turning point in his life to become an even greater ninja.