Jack's purpose is to save his sister. This development will be central to the plot as it plays out.
Claire's experience of the Other's has only been as a threat to her (season 1 and now season 6). She is a perfect candidate for MIBs team cus he plays on one's fear and doubt. MIB nabbed her when he had the opportunity, leaving everyone to think she was dead and Kate subsequently taking Aaron (which would lead to a sad and angry Claire who could kick some ass for MIB in the final season). Claire now has every reason to hate anyone remotely associated with the Others. Aaron's significance is thus not that he is Jacob or the creepy blond kid, but that he was used as a pawn by MIB as a major move in the game.
By convincing Claire to join him, Jack would begin the unraveling of whatever power MIB has over certain people. We have yet to see how Jin will respond to our new Locke, and what he will be told by him. Past theories on this site have mentioned that Flocke is trying to pit certain characters against others in an effort to strenghten his army (e.g. Sun vs. Jin, Jack vs. Claire, Kate vs. Sawyer) therefore making Jacob's team powerless. Past theories have also mentioned that significance of the Littleton-Shephard connection, and this would be a perfect way to explain it.
What better way is there for Jack to redeem himself or obtain closure other than to reunite with his sister and convince her to not listen to MIB. This would be closure for Jack because he would be correcting his father's mistake of abandoning Claire and her mother. Jack will become the way in which Claire will be able to return to her mother and Aaron. His actions with Claire on the island will subseqeuntly help to undo the power that MIB has over his current players (e.g. Claire, Sawyer). For now, I haven't had time to think this through much further.
Thoughts on "infection": It appears that Claire was never "infected" so much as manipulated by MIB. This means it's possible that Sayid has not been infected at all. Perhaps the Other's are just being super cautious with Sayid b/c of what happened with Claire. I assume that's why Jack is waiting and watching Sayid so closely. Plus, why would Jacob bring Sayid to the island only to be killed by the Other's? If Jack sees that Claire is okay, he will know Sayid is okay too.
A few other thoughts: the "Kwon" listed in MIB's cave and Jacob's lighthouse is not one or the other, but both (remember Jacob touched both of them). Kate's purpose on the island is to appeal to Sawyer's softer side so he will not fight for MIB. Sawyer couldn't give a damn about Jack, but could he ever hurt Freckles?