Do you all remember Christian's conversation with his young son?
"Jack, don't choose, cause when you do you don't have what it takes."
Christian knew that his son was an idiot.
Realize that the show is built on paradoxes.....Jack wants to get off the island but he shouldn't.....Jack plans to use the SAT phone, but that may not be a good idea.....Jack loves Kate, but he shouldn't.....Jack thought his dad was a drunk, but he didn't even know his father....Jack trusts Juliet, but should he?
Jack is like one of those kid toys you punch, knock over, it flips back up, and you punch it again. I think that his plan will quickly unravel.