There's a reason he's always adored her story - that sense of refusing to give up permeates it because it's a part of her. It's what gave him the will to hold on for ten years. She's asking him to trust her, in a way - the same way he'd asked her to trust him. (The same trust he'd betrayed, from time to time.)

"I never said I wouldn't help," he protests, glancing at the screens making themselves known. "I wished to see everyone again, after all."

Maybe those two wishes would be strong enough. Hadn't he wished to read about Junghyeok forever, as a child? That might be why these cursed worldlines exist.

Still, he adds, "I just don't want you to get your hopes up if it doesn't work again." I don't want to lie and hurt you again.