Cosette spent the last few days of the summer break with Maxen. They had a talk regarding the setup of their relationship. After all, Maxen regarded Conan with the highest respect he could give to a man, and he didn't want to hide their relationship status. He was prepared to get kicked out and work hard, be better in school, and succeed in life to be able to stand on the same ground as her.
However, Cosette crushed his plans with a simple no.
He might be ready to get kicked out, but not Cosette. She would rather hide it for the time being, for the sole reason she knew Conrad. Her father was aware of Cosette's feelings toward Maxen and she had been very open about it. Moreover, she worked under her father for straight two months.