I've seen a lot of fans theorising that David was supposed to be Jack and Kate's son, that Kate had been pregnant at the end of the series. But I'm not convinced. If he was their son, why did he act as if Juliet was his mother in the flash-sideways? It makes no sense!

I've seen others suggesting that Juliet had also been pregnant when she died, and that David is some amalgamation of that child and Jack and Kate's. But that'd be too weird for me.

Also, I may be absolutely hopeless at working out how much time passes during and between different seasons of Lost, but I'd have thought enough time would have passed between the start of season 5 and the end of the series for Kate to have at least suspected a pregnancy. Wouldn't she have mentioned that to try to persuade Jack to leave with her?