One reason it's so popular is that it fits well with the overall themes of the Harry Potter series. Harry has always been a protector, from protecting his friends from bullies at Hogwarts to fighting Voldemort. Protecting Ginny is just another layer of that. Fanfiction writers use this trope to delve deeper into Harry's character, showing his loyalty and love in a more focused way. It also gives Ginny a role where she can be both strong on her own but also someone who is cherished and protected by Harry, which is a very appealing dynamic for readers.
One great 'Harry is protective of Ginny' fanfiction is 'The Protector's Promise'. In it, Harry is constantly on guard to keep Ginny safe from various threats at Hogwarts. Another one could be 'Harry's Watchful Eye'. It shows Harry's protectiveness in a more emotional way as he fears losing Ginny to the ongoing chaos in the wizarding world.
In some versions, Neville could also be one of Harry's protective mates. Neville, who grows in courage throughout the series, would be willing to stand up against any threat to Harry. And Luna, with her unique perspective and magical abilities, might also be part of Harry's protective group.
Maybe Blaise sees something special in Harry. In fanfiction, it could be that Blaise admires Harry's courage or his unique abilities. He might feel a sense of kinship with Harry despite their differences.
Ginny might support Harry by simply being there for him. In the face of everyone else turning their backs, her presence can be a great comfort. For example, she could sit with him at meals when no one else will.
One possible reason could be miscommunication. Maybe Ginny feels neglected by Harry because he's so caught up in his own heroic deeds and doesn't pay enough attention to her. So she might seek comfort or excitement elsewhere.
Well, it could be that in the fanfiction's plot, Harry has some special qualities or is in a dangerous situation. Edward, being a character with his own set of values, decides to be protective. For example, if Harry has some sort of power that others might want to misuse, Edward would step in to safeguard him. It might also be related to their shared experiences or a bond that has developed between them over the course of the story.