Maybe they run away because they are on a quest that is not approved by the authorities. For example, they might have found a clue about a powerful and ancient magic that could be misused. And they need to find and protect it away from those who might have bad intentions. So they run away to follow the trail of this magic without interference.
In fanfiction, Harry and Luna could run away because they feel out of place. Harry has always been a bit of an outsider, and Luna is often seen as strange. Together, they might decide that they can create a better life away from the judgmental eyes of their peers and the rules of the wizarding society. They could be seeking a place where they are truly accepted and can be themselves.
They might run away because they want to explore the wizarding world on their own terms. Without the restrictions of Hogwarts or the watchful eyes of the Ministry of Magic.
Maybe for love. They might have fallen deeply in love and want to be away from the prying eyes of the wizarding world.
Well, perhaps they run away to escape the chaos at Hogwarts. Maybe they've discovered a dark secret within the school that puts their lives in danger. So they decide to flee and find a hidden place in the Forbidden Forest to stay safe.
They might choose to run away secretly because they want to be alone together. They are in love, and the hustle and bustle of Hogwarts life doesn't give them enough privacy. So, they run away to a quiet place where they can enjoy each other's company without any interruptions.
Love. Naruto may finally realize his true feelings for Hinata and want to be away from the chaos of the village to be with her in peace.
Perhaps in the fanfiction, Ciel discovers some dark secrets about the Phantomhive family or the underworld they are associated with that are so disturbing that he decides to run away. He wants to distance himself from all the evil and corruption, hoping to find a place where he can be free from all the burdens that come with his family name.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Perhaps they are tired of the constant power struggles and drama. Bella has seen a lot of chaos in the vampire world, and Jasper has been through it for a long time. Together, they decide to run away to find some peace. They want a life away from the battles, the territorial disputes, and the never - ending family feuds. They believe that by running away, they can start anew and build a more harmonious existence for themselves.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
Harry might walk away because he has a new mission that he can't share with others. He realizes that to protect the wizarding world in a more fundamental way, he has to go it alone. So, he quietly walks away from his normal life to pursue this unknown and dangerous task.
Some fans like it because it offers an alternative to the canon relationships. It gives a chance to explore a different dynamic between Harry and Hermione, one that might be more romantic or at least a very deep friendship that's different from what's shown in the books. It allows for creativity and new storylines.