Jane had entered the academy without a clear reason
She didn't care about her family's reputation, so she didn't care about the points she had accumulated.
All she wanted once she entered the academy was to kill Allen.
Yet, reality unfolded in ways she hadn't anticipated. Instead of single-minded vengeance, her focus shifted to a new goal: protecting Felicia, someone precious to her brother.
'I know brother's taste in women, he did not regard Lady Felicia as a romantic interest; she had always been akin to a sister in their relationship. And somehow, it makes me think so too,' Jane thought.
She didn't expect Felicia's existence to suddenly become precious to her; that's why she did this duel. Winning became more than a personal victory; it was a means to ensure Felicia's safety. The thought of losing, and consequently failing to shield Felicia, intensified Jane's determination.