The Liu's could not request Wei Yuan to resign because that would be offensive, even though the Master had originally had the intention to do so.
The best solution was to make Wei Yuan resign on his own initiative and write her a reference letter. It did not matter to whom he referred her––she was heading to Langye, anyway. The key was Wei Yuan's being the one to mention his resignation, which would make for a win-win situation.
Jiang Pengji had not thought about that before her visit, but she could tell his plan from his expression. The Master knew what he should do. As a kind teacher, he was genuinely concerned about his student's future.