One possibility is that Harry leaves due to feeling like an outsider still. Maybe he discovers some long - hidden family secrets that make him question his place in the Potter family. He could then leave to seek his own identity away from the family name and all the expectations that come with it.
In a fanfic, Harry might leave the Potter family because he's being wrongly accused of something by the wizarding community. His family doesn't fully support him, so he decides to leave. He then goes on a journey to prove his innocence on his own, facing many challenges along the way and growing stronger without the family's protection.
Perhaps he leaves to explore the Muggle world. Harry has always had an interest in Muggles. After the war, he realizes he wants to experience life without magic for a while. He could go to university in a big city like London, study a Muggle subject like history or literature. He'd make new Muggle friends and try to fit in, all while still having his magical abilities hidden, which would add an interesting dynamic to his new life.
One possibility could be that Harry Potter leaves Earth to explore other magical realms in the universe. Maybe he discovers a planet where magic is used in completely different ways than on Earth. He could encounter new magical creatures and make friends with beings who have powers he's never seen before.
One possibility is that Harry leaves Hogwarts to go on a solo adventure to find more about his family's past. He might travel to different wizarding communities that his parents were associated with, uncovering secrets along the way.
The family ring could be a magical heirloom that holds the secrets of the Potter family's past. Maybe it has the power to unlock hidden chambers or memories. It could be a key element in a battle against dark forces, with the ring's magic being crucial for victory.
Maybe Harry leaves England to explore the wizarding world in other countries. He could go to France to study different magic spells at Beauxbatons Academy. Or perhaps he travels to America to help the MACUSA (Magical Congress of the United States of America) deal with some dark magic threats.
One possible plot could be that Harry Potter discovers he is pregnant (through some magical means perhaps) and decides to leave England because he wants to protect his unborn child from the dark forces that still lurk in the country. He might go to a far - off magical land where he can raise the child in peace and secrecy.
One possible plot could be that Harry leaves Hogwarts to hunt down the remaining Death Eaters on his own. He might feel that he can't put his friends in danger anymore and takes it upon himself to rid the wizarding world of the last remnants of Voldemort's followers.
Perhaps they leave because they discover a new threat that the ninja villages are not taking seriously. Naruto and Sasuke decide to take matters into their own hands. They travel to different places, gathering information and allies. Their relationship also evolves during this time, from just comrades to true brothers who understand each other completely.
Well, perhaps the story could start with baby Harry's transformation being a mystery at first. Dumbledore and others might be trying to figure out what's wrong with him. As he grows up, he has to face the discrimination of the wizarding world because of his werewolf status.
The fanfic could also be about how Harry's past experiences shape his parenting. Given his own difficult childhood, he would be extremely determined to give his baby a loving and secure environment. He might teach the baby about the importance of friendship and courage from a very young age, and the baby could grow up with a strong sense of justice, much like Harry did.