Perhaps Hermione has her own plans regarding Runes. For example, she might have wanted to study Runes with Harry in a particular way or at a certain time. When Harry starts taking Runes on his own or in a different manner, it disrupts her plans, leading to her anger. Also, she could be worried that Harry's approach to Runes might get him into trouble or affect his overall academic progress in a negative way.
He might be confused at first. Harry isn't always the quickest to understand Hermione's motives right away. So he could just stand there, looking at her with a puzzled expression on his face, not really knowing what he did wrong.
One possible fanfic could be where Harry discovers a hidden connection between Runes and Arithmancy that helps him in his battle against Voldemort. Maybe he finds ancient runes that, when decoded using arithmancy principles, reveal a powerful spell or a secret weapon.
In some fanfictions, Harry might be angry with Ron and Hermione if he feels they are keeping secrets from him. For example, if they discover something important about Voldemort's plans but don't share it right away, Harry could get angry. He's used to relying on them and when that trust is broken, even if it's a misunderstanding, his anger can flare up.
There could be a fanfiction where Harry has discovered a new type of flying spell or device. He decides to share this experience with Hermione. So, he takes her flying at night, when the stars are out. They fly over the Black Lake and Hermione is in awe of the beauty she's seeing from above. The flight becomes a special moment for them to bond even more as friends.
There might be a fanfiction where Harry Potter takes Runes as an elective instead of something like Divination. In this story, he delves deep into the study of Runes, and with the help of Hermione, they uncover secrets about Hogwarts that were written in Runes long ago. They could find that the Runes hold the key to a powerful magic that can protect the school from an impending doom.
One great fanfic could be where Harry discovers a hidden connection between Ancient Runes and Arithmancy that helps him in his battles against Voldemort. Maybe he finds ancient spells inscribed in runes and uses arithmancy to decode their true power.
A really interesting one is 'Fractured Bonds'. Here, Harry is angry at Hermione because he believes she has been keeping secrets from him. It delves deep into their relationship, exploring the themes of trust and loyalty. As the story progresses, we see both characters grow and learn from the situation, and eventually start to repair their damaged friendship.
One interesting plot might be where Harry is the only one who can see the true meaning of certain runes because of his arithmancy skills. This leads him to a hidden chamber in Hogwarts where he discovers a powerful artifact that has been lost for centuries. And this discovery sets off a chain of events that involve him having to protect the artifact from dark wizards while also trying to understand its full potential.
A major reason could be differences in their approaches to fighting the dark forces. Maybe in the fanfic, Hermione wants to use a more diplomatic and academic approach, Ron is hesitant and just wants to follow the status quo, and Harry wants a more direct and action - based approach. Their inability to reconcile these differences can lead to Harry being angry. For example, when they are planning how to deal with a new dark wizard threat, their arguments and lack of compromise can make Harry frustrated and angry with them.