In some fanfictions, Harry Potter might be angry at the Order because he feels they are keeping secrets from him. He is used to being in the thick of things and when the Order withholds information, it can make him feel left out and untrusted.
One common theme is betrayal. Harry often feels betrayed by those he trusts, like the Ministry of Magic or certain teachers, and his anger stems from that. For example, in some fanfics, he discovers that they have been using him for their own purposes.
Perhaps a fanfiction where Harry is angry due to the danger the Goblet of Fire has put his friends in. He realizes that just by being a part of the Triwizard Tournament, his enemies might target his friends to get to him. His anger could drive him to take extra precautions to protect them, and also make him more determined to succeed in the tournament so that he can prove that he's not a coward and that he can handle whatever comes his way.
You can start by looking on popular fanfiction websites such as Fanfiction.net or Archive of Our Own (AO3). These platforms have a wide variety of fanfictions, and you can use their search functions to specifically look for 'angry harry potter' fanfiction. Just type in the relevant keywords and browse through the results.
One example could be a fanfiction where Harry is angry at the Ministry of Magic for their continued interference in Hogwarts affairs. He might take matters into his own hands and start a rebellion of sorts among the students to fight for the school's independence. Another could be Harry being angry with Draco for some new scheme and they engage in a more intense rivalry than in the original books.
In fanfiction, Harry Potter might be angry if his friends are in danger and no one seems to be taking it seriously. He's very protective of his friends, like Ron and Hermione. So if some authority figures in the story are being dismissive of the threats his friends face, that would surely make him angry.
In a 'Harry Potter gets angry' fanfiction, he could be enraged when he realizes that some old pure - blood families are still trying to undermine the new order at Hogwarts. His anger might fuel him to confront these families directly, leading to intense magical duels and a struggle for the future of the wizarding school.
One common theme is justice. Since Harry is angry, it often involves him seeking justice for wrongs done to him or his friends. For example, if a character was wrongly accused in Hogwarts, Harry's anger would drive him to clear their name.
Another reason could be that Harry sees the Order as being too cautious or old - fashioned in their approach to fighting Voldemort. He might believe that their traditional methods are not enough to defeat Voldemort quickly and effectively, and this lack of progress makes him angry at them.
Maybe he feels that the Order is keeping secrets from him. In many fanfictions, Harry can be a character who values honesty and when he discovers that the Order, which he may consider an ally, is hiding things from him, it can make him angry.