One possible reason could be that he feels misunderstood by his family or friends. Maybe he has some secrets that he's afraid to share, and the fear of being judged makes him run away.
Perhaps he discovers some dark truth about the superhero world he's in. It could be something related to the Justice League or Gotham City that shakes his beliefs so much that he wants to get away from it all. He might need time to process this new information and figure out what he wants to do, so he runs away to have that space.
Tim Drake walking away in fanfiction could be a way to explore his character in a different light. It could show his independence. He might be walking away to start his own journey, to figure out who he really is outside of the shadow of the Bat - family. In some fanfictions, this could lead to him developing new skills or making new allies. It gives the writer a chance to take the character in a unique direction, away from the more traditional storylines.
One possible ending is that Tim Drake realizes he made a mistake by walking away and returns to his old life. He might come back with a new perspective and be even more effective as a hero. Another ending could be that he finds a new purpose outside of the superhero world and is content with his new life. He could be living a normal life, but still using his skills in a different way, like helping the local community in non - superhero ways.
In some fanfictions, it could be due to personal growth. Tim Drake might have outgrown the role of Robin or the shadow of Batman. He may want to explore his own identity and capabilities independently, away from the Bat - family. He could feel that staying with Batman is holding him back from reaching his full potential as a hero.
Perhaps Naruto discovers something about Itachi that the rest of the world doesn't know and he needs to run away to protect that secret. It could be a powerful jutsu or a message that could change the balance of power in the ninja world.
One reason could be that the writer wants to explore new storylines without his character. Maybe they feel his arc has reached a natural conclusion in their fanfic universe. For example, if the story has been centered around Tim Drake's detective work for a long time, the writer might decide to shift the focus to other characters by having him leave.
It could be due to a personal betrayal. For example, if he discovers that another member of the Bat Family has been hiding something important from him that makes him feel he can't trust them anymore. This would make him want to leave and create his own identity away from the family. In fanfiction, this kind of emotional turmoil can drive the story forward.
Another reason could be that she wants to explore the world on her own terms. In the fanfiction, Mirabel may be tired of always being in the family's protective bubble. She desires to see what lies beyond the village and the mountains, so she runs away to start her own adventure.
In the 'run away children story', sometimes children run away because of a lack of understanding or communication at home. Parents might be too strict or not pay enough attention to their children's feelings. The children then think running away is the only way to get noticed. Also, problems at school like bullying can lead to children running away. They may feel that they can't face the bully anymore and choose to leave.
A common reason could be a desire for adventure. Legolas, being an elf, might feel the need to break free from the monotony of his daily life. So he runs away to explore new lands and have exciting experiences.
Maybe Pikachu is feeling neglected by its trainer. If the trainer has been paying more attention to other Pokemon or is too busy with something else, Pikachu might decide to run away to get some attention.