I think it's his way of getting Kate to focus on him rather than Sawyer, like a "He chose to stay (away from you) I chose to leave (and be with you)." sort of thing. I think it's just the fact that she's doing something for Sawyer, thereby doing something that is reminisent of their life on the island (which they've been lying about off-island), and also something to do with his former love rival, is what's drove Jack over the top. Let's not forget that Jack also goes through a minor breakdown in these flashbacks - possibly this is shortly before the way he was at the end of the S3 flashforward?
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