Perhaps he was in a fight against a group of Death Eaters. They might have used some kind of dark magic that backfired on Harry, causing him to lose his arm while trying to protect others.
It could be due to some kind of accident in a dangerous magical experiment. He might have been trying to create a powerful charm or potion and something went horribly wrong, resulting in the loss of his arm.
Maybe he was in a dangerous duel with a powerful dark wizard. The dark wizard could have cast a spell that was specifically designed to maim or disarm in the most literal sense.
In some fanfictions, it could be a gift from a parallel magical dimension. There could be a race in this other dimension that is very advanced in combining magic and metalwork, and they see Harry as a hero worthy of such a gift. The metal arm could then hold the secrets and powers of that dimension, which Harry has to figure out how to use to save the wizarding world.
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 reason could be safety. Some fanfiction authors might think that Hogwarts is too dangerous for Harry, so they make him homeschooled to keep him out of harm's way.
Some fanfiction writers may have a different vision for Harry Potter's character. They might see him as more of a diplomat or a healer within the wizarding world, rather than a fighter. So, they write stories that reflect this different view of the character, where he uses his wits and other skills rather than engaging in physical or magical combat.
One reason could be to explore the darker side of human nature. Even though Harry is a hero in the original series, fanfiction writers might want to see how he would be affected if he was pushed to his limits. Another reason is to create a more complex and controversial storyline. It grabs readers' attention as it goes against the normal perception of Harry.
One reason could be a reaction to the Ministry of Magic's mismanagement. In the original story, the Ministry often made mistakes and had corrupt elements. In fanfiction, this could lead to Harry becoming an anarchist as a way to oppose such a flawed system.
One possible reason could be his past experiences with some cruel adults, like the Dursleys. They treated him horribly, so in fanfiction, this trauma might make him generally fearful of adults. Another reason could be his experiences with certain authority figures at Hogwarts who may have been strict or unfair, which could be exaggerated in fanfiction to create a fear of adults.
One reason could be his over - use of powerful magic spells. If he uses spells like the 'Geminio' spell (used to duplicate objects) on valuable items without any control, it could flood the market and make the items worthless, thus ruining the economy. For example, if he duplicates rare magical potions in large quantities, the potion - making industry would collapse as there would be no need to buy them at regular prices.
There are several possible reasons. Firstly, in the realm of fanfiction, there is a desire to push boundaries. Fans want to see how far they can deviate from the original story while still using the familiar characters. Secondly, it could be a way to express personal views on gender and sexuality. By creating a scenario where Harry Potter is a crossdresser, they are making a statement about the fluidity of gender roles. Additionally, it might be a form of artistic experimentation. Writers may be curious about how the story would change if such a significant alteration was made to the main character's appearance and identity.
One possible reason could be that he is wrongly accused of using dark magic. In some fanfictions, the Ministry of Magic might be more corrupt or easily influenced, and they could frame Harry for something he didn't do, leading to his expulsion.