Being the daughter of a famous fashion pony, Jewel followed exactly. Ponies around looked up to her, but unfortunately she doesn't think the same way about them. Jewel lives in belief that since her mother was an element of harmony, she would be as well. Bragging about her mother's status and how she is the next element, she not only have followers, but she made enemies as well.
Blue Moon never wanted people to know that Rarity was his mother. He was embarrassed that his mother, despite being an element, cheated on his father. Never once did she visit him either when she clearly had visitation rights. Blue Moon turned to books and studies to fill in the emptiness in his heart.
Blue Moon, Jewel and Emerald were all invited to join the School of Friendship. Jewel and Emerald immediately agreed and wanted to attend as soon as possible. Blue Moon only attended because Fancy Pants had told him that having friends might help him with his troubles. Not only that, but Fancy Pants trusted Starlight Glimmer to look after them and make sure nothing bad ever happens.
After hearing what happened with Rarity and Fancy Pants, Starlight was skeptical of even accepting Jewel and Emerald. Especially after seeing how they behaved when they first went to the school to register for classes. Even with that kind of first impression the twins left, Starlight convinced herself to take them in and say that maybe they can change.
After two months, Starlight was starting to regret her decisions. Jewel and Emerald showed no signs of changing. Jewel was constantly picking on Blue Moon while Emerald worked on trying to take Blue's friend away from him.
If they actually attended class, they should know that the only ones that was getting isolated was them.