Maybe he has friends or relatives in America who can offer him a place of refuge. In fanfiction, it's common to create new relationships for characters, and he might be running towards those connections. Also, the wizarding community in America could have something unique to offer him, like a different approach to magic that he wants to explore.
One reason could be to escape the public spotlight. After the war, Harry is a hero and Ginny is his girlfriend. They might feel overwhelmed by all the attention and want a quiet life, so they run away.
Maybe Harry feels a sense of guilt. In the context of the war, he might think that he's failed in some way by getting into this unexpected situation. He could believe that his new condition might put others at risk or that he's no longer the hero everyone expects him to be. So, to protect others or to avoid the shame, he decides to run away.
One possible reason could be that he is suffering from post - traumatic stress disorder. After all he has been through, he might want to isolate himself from the wizarding world to heal. Another reason could be that he feels a sense of guilt for those who died in the war, and disappearing is his way of punishing himself.
One possible reason could be the trauma they both endured during the war. Ginny might be frustrated with Harry's withdrawn behavior as he tries to deal with his own demons. Maybe he's been neglecting their relationship in his post - war self - reflection.
One reason could be the trauma he endured during the war. He witnessed so much death and destruction that he might feel the need to escape it all. Maybe he wants to get away from the constant reminders of his friends who didn't make it.
One possible reason could be miscommunication. Maybe Harry made a decision during the post - war rebuilding without consulting Ginny, and she felt left out or disrespected. For example, if he agreed to some dangerous mission without telling her.
One possible reason could be the trauma they both endured during the war. Harry especially might have post - war issues that make it difficult for him to be in a relationship. He could be haunted by the deaths he witnessed and feel unworthy of love. Ginny, on the other hand, might have grown tired of waiting for Harry to fully recover. Another reason could be the different paths they want to take in life post - war. Harry might feel a strong sense of duty to help rebuild the wizarding world in a way that doesn't involve a relationship, while Ginny may want a more stable family - oriented life right away.
It could also be that Harry himself is so traumatized by the war that he isolates himself. He might push people away, thinking that he's a danger to them. As he withdraws, others might misinterpret it as him not wanting their company and gradually abandon him.
He might discover new magical communities in America. Maybe he'll meet some interesting witches and wizards who have different ways of using magic compared to those in Britain.
Maybe they run away because they are tired of the constant danger at Hogwarts. They've faced so many threats, and they just want a break. So they run to a peaceful place where no one knows them.