Yeah, I guess my original question is when do people get crossed off?
At some point, Jacob gives up on them. But they all start out as possible candidates ... and they're already flawed before they even come to the Island, right? (Or are they pure at the moment Jacob comes to visit them at some crucial moment and then they subsequently go wrong?)
But once they get the Island, "their past doesn't matter", right? So if they're still viable candidates when they get to the Island, then they get crossed off because of their actions on the Island. Their behavior in the new environment doesn't change and at some point after they've come to the IslandJacob crosses them off.
For Kate, I can go with its being taking Aaron "for her own sake" rather than for Aaron's sake, which the show has made a point of saying.