They could be running away due to a misunderstanding. Maybe there was a false accusation against them, and instead of facing a trial or persecution that they believe would be unfair, they decide to run. In addition, it might be related to family issues. There could be some internal conflicts within the wizarding families that they belong to, and they feel that leaving is the best solution to avoid more troubles. Also, they may want to protect someone else by running away. If there is a threat to a loved one, they might lead the danger away from that person by disappearing.
Well, perhaps they run away because they discover some dark secrets about the wizarding world that others don't want them to know. They might fear for their lives if they stay, so they choose to flee. It could also be that they are simply seeking adventure. The daughter of Harry and Sirius might inherit their adventurous spirits, and they both decide to run away to explore the unknown parts of the wizarding world and beyond.
One possible reason could be to escape from false accusations. In the 'Harry Potter' universe, Sirius was wrongly accused of betraying the Potters. So in the fanfiction, he might run away to avoid being captured and to find a way to prove his innocence.
Perhaps in fanfiction, Harry runs away from the Dursleys because he discovers a new threat that the Dursleys won't protect him from. He realizes that he has to take matters into his own hands and leaving is the only option. Also, he could be running away because he has made some new friends in the wizarding world who offer him a better alternative to living with the Dursleys.
One reason could be the trauma he endured during the war. He witnessed so much death and destruction that he might feel the need to escape it all. Maybe he wants to get away from the constant reminders of his friends who didn't make it.
Well, she might run away because she feels overshadowed by her father's fame. Everyone always talks about Tony Stark, Iron Man, and she may feel like she's just an afterthought. Maybe she wants to find her own identity away from the Stark name.
Well, perhaps they ran away because they were tired of all the rules and restrictions at Hogwarts. Harry had always had a bit of a rebel streak, and Hermione might have finally agreed that they could achieve more on their own. Also, it could be related to a prophecy that they thought was best dealt with away from the prying eyes of their friends and teachers.
One reason could be to escape the constant danger at Hogwarts. Maybe there's a new dark wizard threat that the school can't protect him from. So he runs away to find a safer place to hide and train on his own.
She could be running away due to family pressure. Her family might be forcing her into an arranged marriage or pushing her to join a certain dark - leaning group within the Slytherin community.
One possible reason could be that she feels overwhelmed by her responsibilities. In the world of Equestria, Twilight has a lot on her plate, like studying magic, taking care of Spike, and helping her friends. In fanfiction, the writer might explore the idea that she just needs a break from it all and runs away to find some peace.
Maybe she feels left out in the family. In the Encanto story, Mirabel is the odd one out not having a special gift. This could make her feel so alone and unwanted that she decides to run away.
She might run away because of a conflict with her friends or team members. Maybe there was a misunderstanding or a disagreement that she couldn't resolve at that moment, and running away seemed like the best way to avoid further confrontation.