What if Aaron is really Sawyer's baby and that is why Jack doesn't want to see him? When Kate's mother said she wanted to see her grandson it proves that Kate is claiming Aaron to be her own child. Did she adopt the kid from Claire? How could she, being a fugitive from the law. I think that she gave birth to this child. Her mother also said that for the past four years the doctors have been telling her she only had 6 months to live. What if that was a clue so that we could piece together the fact that there has been enough time lapsed for Kate to have given birth to this boy???

My best guess is that something went down on the island between Jack and Claire... something that makes him not want to see Aaron. Kate invites him over... and he says that he can't come over. Or maybe Claire forced Aaron on Kate...

But yes, Claire was warned that if she doesn't raise Aaron that he is destined to be an evil presence... interesting. Hopefully she was with him long enough.

The overall timeline of from where we are now to the rescue is not completely filled in. Possibly an event that caused kate and jack to be more closer to the baby?

Why Jack doesn't want to see the baby? Does he know that Claire is his sis???

The warning was that no one else should raise the baby but Claire, or bad things would happen. That was why he he was so against the adoption, and made her get on the plane, the psychic knew the plane would crash and she would raise Aaron.