One reason could be to escape the constant scrutiny and expectations that come with being 'The Boy Who Lived' in Magical Britain. He might feel suffocated by the fame and the never - ending battles against the Dark Arts in his homeland. Another reason could be a quest for new magical knowledge. Magical Britain has its own set of magical teachings, but there could be other, more esoteric forms of magic in other parts of the world that he wants to explore. Also, he might be running away from a personal tragedy or a broken relationship. Maybe a falling - out with his friends or a loss of someone dear to him makes him want to start anew elsewhere.
One possible reason could be extreme disillusionment with the wizarding society in Britain. Maybe he faced so much political intrigue, discrimination, or ungratefulness from the people he had saved that he just couldn't take it anymore. For example, if the Ministry of Magic continued to be corrupt and turn a blind eye to dark magic activities, it might push Harry to abandon the place.
One reason could be that he discovers a new threat and decides he can't stay with the Dursleys any longer for their safety. Another might be that he simply can't bear their mistreatment anymore and finds an opportunity to escape.
One reason could be that the official Harry Potter canon is so extensive and detailed that it overshadows fanfiction. The original story has such a rich world, characters, and plotlines that it becomes the main focus for many fans, leaving less room for fan - created stories.
One possible plot could be that Harry discovers a dark secret about the Ministry of Magic, like they are using dark magic themselves to control the wizarding population. So he decides to expose them and in the process, the chaos that ensues leads to the destruction of magical Britain as it was known.
One possible reason could be a misunderstanding. Maybe there was a miscommunication between them, like Ginny thought Harry was still too preoccupied with his past traumas and not fully committed to their relationship. Another reason might be external pressure. In some fanfictions, there could be outside forces, such as dark wizards threatening Ginny and she leaves Harry to protect him.
One possible reason could be the corrupt system in Magical Britain. In some fanfictions, the Ministry of Magic is shown as being full of bureaucrats who are more concerned with maintaining power and the status quo rather than doing what's right. For example, they might be slow to respond to real threats or they could be discriminatory towards certain groups, like Muggle - borns. Harry, having grown up in a non - magical world and having a sense of justice, would naturally despise such a system.
Perhaps in the fanfiction, Harry Potter runs away from Britain because he is disillusioned with the way the Ministry of Magic operates. There could have been a major event where the Ministry fails him or betrays his trust. Also, he may be seeking a place where he can explore his magic without the constraints and expectations that come with being 'The Boy Who Lived' in Britain.
The theme of breaking free from expectations is quite common. In Magical Britain, Harry has so many expectations placed on him because of his status as 'The Boy Who Lived'. When he leaves, he can be his own person and not be defined by those labels. Also, the exploration of different magical cultures is a big theme. He gets to see how magic is practiced in other parts of the world, which is really fascinating.
One interesting scenario could be Harry Potter starting a new life in the Muggle world and using his magical skills in secret to help people. For example, he might use magic to heal the sick in a Muggle hospital without them knowing. Another could be him exploring different magical cultures outside of Britain, like those in Asia or Africa that are not much explored in the original books. He could learn new spells and magical techniques and bring them back to the wizarding world in the future.
In some fanfiction, Harry leaves to seek more powerful magic. He realizes that the magic in Britain is somewhat limited in the fight against Voldemort. So he travels to other places, like ancient magic - rich regions in Asia or Africa, to find a way to defeat Voldemort. He hopes that by leaving, he can gain the upper hand in the battle.