It could also be due to a false accusation. Perhaps someone framed him for something he didn't do, like stealing important artifacts from the school. And in the world of RWBY, if he was found to be secretly associated with a group that the school considered dangerous, that would also lead to his expulsion.
He might first feel a great sense of despair and self - loathing. But then he could start training on his own, determined to prove the school wrong. He could look for a mentor outside of Beacon, someone who believes in his potential.
One possible reason could be his unruly behavior. Naruto is known to be a bit of a troublemaker in the series, always pulling pranks. In fanfiction, this might be exaggerated, and the orphanage might not be able to handle it anymore. Another reason could be that he's suspected of being involved in something dangerous or illegal, even if he's innocent. For example, if there are strange incidents around the orphanage and Naruto is the easy target to blame because of his reputation.
One possible reason could be his prankster nature. Maybe he played one too many harmless but annoying pranks on the staff or other orphans, and they decided they'd had enough. Another reason might be the fear of the Nine - Tails within him. Even if the people in the orphanage didn't fully understand what it was, they could sense something dangerous about Naruto and wanted to distance themselves from him for safety reasons.
One possible reason could be a serious rule violation. For example, if Harry was wrongly accused of using dark magic within the Gryffindor common room. Another reason might be that he was framed for stealing the Gryffindor sword. It could also be due to a conflict with other Gryffindor students that got out of hand and the house decided they couldn't keep him anymore.
Maybe he's falsely accused of stealing important Gryffindor artifacts. For instance, if the Sword of Gryffindor goes missing and Harry is wrongly blamed, the house might decide to kick him out. It could be part of a plot by a jealous student or an outside force trying to disrupt Hogwarts.
Maybe he was blamed for some trouble he didn't actually cause. For example, if something went missing in the orphanage and the caretakers wrongly thought Naruto took it.
Perhaps she was kicked out due to personal conflicts within the pack. If there were other members who didn't like her or were jealous of her for some reason, they might have spread false rumors or convinced the pack leaders to expel her. It could also be that she was in a relationship that the pack disapproved of, and as a result, they decided to kick her out.
Perhaps Percy was kicked out because of a prophecy that the camp elders misinterpreted. They thought that Percy's presence would bring great danger to the camp, so they made the hasty decision to expel him. It could also be that there was some sort of political intrigue within the camp. Some powerful figures at the camp might have seen Percy as a threat to their power and influence, and so they fabricated reasons to get him kicked out.
One reason could be causing disruption. If the 'crusade' involved making a lot of noise, blocking hallways, or disturbing classes, the school would likely take action.
One possible reason could be that she has different beliefs or values from her family. For example, if her family follows a very traditional path and she wants to pursue something more modern or unorthodox like a career in a non - traditional field that the family doesn't approve of.