Responses
I think he wants her on board with this whole 'education reform' and 'counselling is useless, avoidance is best' thing. Her father is a politician as well, so he could use that through her. If this scandal forces her to resign from counselling at the university, she's free to work with Seonghyun.
Even though she initially declined, she may have no choice but to work with Seonghyun if she has to quit. Baek, knowing that he wants her to work with him wants to resign instead of her, because he doesn't want to give Seonghyun what he wants.
What the hell is Seonghyun UP to? He got mad Song Sun declined working with him so he orchestrated her patients suicide so she'll loose faith in herself? That's some supervillian shit. And what even happened between him and Baek anyway?