I think Ben used that to get Kate to pay attention to Jack and thus to him. I expect he has some other case to make or blackmail to threaten, and just needed to actually get to Kate to make it. After all even if Kate feels the need to bail out with Aaron to keep him, there are hundreds if not thousands of places which would be preferable for her than the Island. If it was just the pressure of losing him she'd be more likely to head to Mexico or something.