In the fanfiction world, Harry could be disillusioned with the Hogwarts system. Maybe he thinks the teaching methods are old - fashioned or the rules are too strict. He may believe he can learn more about magic on his own or in a different environment and thus doesn't want to go to Hogwarts.
Perhaps he has seen a dark future for Hogwarts in a vision. He might think that by staying away, he can avoid that future or protect himself from some unknown danger. In fanfiction, there are often new and creative plotlines like this.
One reason could be that he has fallen in love with someone outside of Hogwarts and wants to stay with that person instead. He may feel that Hogwarts will keep him away from his beloved.
One possible reason could be that in the fanfiction, his family might have decided to keep him away from the wizarding world for his safety. Maybe they feared the dark forces at Hogwarts, like Voldemort's followers.
One reason could be that he wants to experience a normal life. In the wizarding world, he is constantly in the spotlight as 'The Boy Who Lived'. At a Muggle school, he might be able to blend in and just be an ordinary kid for once.
In this fanfiction, it could be that Harry has a falling - out with Dumbledore or other important figures at Hogwarts. This makes him feel unwelcome or betrayed, leading him to choose not to go to Hogwarts and seek another path in the magical world.
In some fanfictions, there could be a change in the Hogwarts admission policy. Maybe they found some supposed flaw in Harry's magical abilities or his background that led to his admission being revoked at the last minute, so he didn't arrive at Hogwarts. Also, it's possible that some other powerful magic was at work. A powerful wizard or witch could have cast a spell on Harry that made him forget about Hogwarts or made it so that he couldn't physically reach the school.
One reason could be that he doesn't like others taking creative liberties with his story. He might feel that it's his story and only the original version should be the 'true' one.
One possible reason could be fear. Maybe he's heard some scary rumors about Hogwarts, like the Forbidden Forest being full of dangerous creatures. Another reason might be that he doesn't want to leave his normal life behind. He has friends in the Muggle world and he might be reluctant to give that up for a world full of magic that he doesn't fully understand yet.
One reason could be that he's being hidden by some powerful magic from a group that wants to use him for dark purposes. Maybe there are dark wizards who know of his future importance and want to either kill or control him, so a good wizard has made him disappear.
One reason could be to search for a powerful magical artifact outside of Hogwarts that they believe is crucial for defeating a new dark threat. In fanfiction, they might feel that Hogwarts has become too dangerous or restricted in terms of resources for their mission.
Maybe he leaves because of a conflict with the Hogwarts staff. If the new headmaster or some teachers start implementing rules that Harry believes are wrong or unfair, like restrictions on defensive magic classes, he might decide to leave in protest.