It could be that Harry finds out about Dumbledore's secrets regarding the Deathly Hallows. If Harry thinks Dumbledore was more interested in the Hallows for his own purposes rather than for the greater good, it might make him hate Dumbledore.
Yes, there might be some out there. Fanfiction is a vast and diverse world where writers explore all kinds of alternative scenarios. Some writers may create stories where Harry Potter hates Dumbledore for various reasons, such as feeling manipulated or betrayed by Dumbledore's actions. However, this goes against the general relationship portrayed in the original books, which is why it's an interesting and somewhat controversial topic in fanfiction.
This type of fanfic might shift the focus from the fight against Voldemort to the internal conflict between Harry and Dumbledore. It could explore different character traits of both of them that were not as prominent in the original. For example, Harry's potential for anger and Dumbledore's more flawed side.
Perhaps Dumbledore is shown to have a secret alliance with Voldemort in the fanfiction. Harry stumbles upon evidence of this and is filled with rage and hatred. Or maybe Dumbledore had been manipulating Harry's emotions and actions from the very beginning to fit his own plans for the wizarding world, and once Harry realizes this, his hatred for Dumbledore grows. It could also be that Dumbledore has been hiding a powerful magical artifact that could have saved many lives but didn't, and Harry blames him for it.
One reason could be secrecy. If Harry finds out that Dumbledore has been keeping major secrets from him all along, like about his family or his true role in the wizarding world, he might start to hate him. Another reason could be manipulation. If it seems that Dumbledore has been manipulating Harry's actions for his own gain, that would be a valid cause for hatred in fanfiction.
One possible event could be that Dumbledore fails to protect someone Harry loves dearly. Like if a close friend of Harry's was killed while under Dumbledore's supposed protection, Harry would hold Dumbledore responsible. Another event might be if Dumbledore lies to Harry about his family history. For example, if he hid some important information about Harry's parents that would change Harry's perception of them.
The theme of disillusionment also often appears. Harry, who once idolized Dumbledore, now sees him in a new light. He realizes that Dumbledore is not the perfect mentor he once thought, and this realization leads to his hatred. This can be explored in various ways, such as through flashbacks or interactions with other characters who have different views of Dumbledore.
One common scenario could be when Dumbledore fails to protect someone she loves. In the fanfic, if her best friend or family member gets hurt due to Dumbledore's inaction, she would hate him. For instance, if there was a dark wizard attack and Dumbledore didn't send enough help.
Well, it can change the plot significantly. For starters, she might not follow Dumbledore's instructions blindly. Instead of going on quests or facing challenges that Dumbledore sets for her, she could rebel and take her own path. This could lead to her allying with different characters, perhaps those who are also against Dumbledore's ways. For example, she could team up with some of the more rebellious Slytherins who have their own issues with Dumbledore's leadership at Hogwarts.
In the 'Harry Potter' fandom, this would be a very controversial concept. Dumbledore is often seen as a mentor and a powerful, positive figure. Having Harry Potter destroy him goes against the general perception of their relationship in the original series. However, in the realm of fanfic, some might explore such a dark and alternative take as a way to examine different character arcs and what - if scenarios, but it would likely be met with a lot of resistance from purist fans.