Black tiger wants white tiger and MC to break up. These are the "negotiations" where MC is trying to convince black tiger that white tiger will be happiest with him. As for the why, it's forcing the MC to confront his feelings, and make him develop a solid stance on his relationship with white tiger, and what he wants to do going forward...in theory. Honestly, this arc has felt a lot like water circling around a drain so far; a lot of cyclical dialogue, with no real progress. It feels kind of pointless, the way it's going about things.