It's true that without all the back story, it's hard for Sinclair to give him a reason why she might not, harder still to understand why Jack thinks she should.

"I don't know that she doesn't," he says. Improvising. If you say vague enough things, eventually you'll be led in a clearer direction. "Maybe she did at some point, but she's having a little trouble trusting you. But she's giving you a way to fix it, and I don't believe she would bother if she didn't care at all."