Temperance Brennan and Jack Shephard don't have much in common except that they're both very smart people (hey, they're both doctors) with little bedside manner who have been partnered with a street-smart 'loose cannon' with ties to the law (Seely Booth is FBI; Kate Austen is a former Fugitive) and have to work with a rag-tag band of folks to solve mysteries.
And they can both be extremely slow when it comes to their relationship with their partners because of the trust and love issues that their parents have cursed them with.
In 'The Cinderella in the Cardboard' Brennan and her partner Booth disagree on the merits of marriage and, a step beyond that, the ability for a human being to invest themselves in another human being entirely for the rest of their lives. Brennan finds it irrational and, given the statistics of divorce in the world today, one might be keen to agree with her, but she herself has taken offense to the mere act of other people working with Booth on a temporary basis. It reminds her that their arrangement was intended to be temporary and that they've taken it to levels far beyond the original agreements made between the Jeffersonian and the FBI.
By the end of the episode, despite her impassioned arguments to the contrary, she's realized that her reliance on the logic that drives her investigations and leads to hard facts and evidence isn't necessarily relevant to the workings of the human mind, nor is it applicable to the whims of the human heart. That people can develop connections that are so intricate that they can, in fact, yield life-long bonds and, in some cases, happy marriages is no longer something she questions, but – in spite of her assertion that it is irrational – something she is jealous of.
What she is incapable of or unwilling to understand just yet is that she's already involved in several relationships that are constantly expanding her view on humanity and just how illogical it all truly is. The mere fact that in all matters of chaos she finds herself inexplicably drawn to Booth for comfort should be proof enough for this scientist that she has no reason to be jealous of the willingness of her friends to immerse themselves fully into the lives and hearts of others, because she already has.
She just has to be willing to accept that she has.
With Jack, the problem stems from the fact that he HAS immersed himself in another person, but the demons of the past he had yet to let go of caused their relationship to come apart. Back on the island after three years off, he returns estranged from Kate, having let their engagement fall apart because of his inability to trust that Kate's secrecy, about her meetings with Cassidy and Clementine, was never meant to do any harm.
Having cleaned up from his drug and alcohol addition to return, Jack is in a much clearer state of mind and during 'Some Like it Hoth' he approaches two people about Kate with the knowledge he gained through his own mistakes with her. When Roger Linus drunkenly enters the Dharma classroom Jack has cleaned for him, he announces his suspicions about Kate because she's taken a keen interest in his son. While Jack could have told him that Kate had just "lost" her own son and that she was simply extending an olive branch to someone in a similar situation, he tells Roger that he's had a bad day, had a few beers, and that can alter a person's perception of reality. He knows firsthand, and when he tells Roger that Kate meant no harm in her gesture, he says it with certainty, but also with a little regret.
Jack knows Kate, as he tells Roger, and maybe he's thought back on a lot of her decisions and realized that just like his actions on the island that Sawyer belittled him for a few episodes prior, Kate never means any harm. And it's this idea he carries with him when Sawyer attacks Kate for trying to comfort Roger to begin with. "Her heart's in the right place," Jack tells him, and just as quickly as Sawyer can snap back, "Well, where's her brain at?" Jack can attest to the fact that sometimes the heart acts quicker than the mind and sometimes it can cause a lot more damage than good.
Where Brennan is guided by her mind; Jack has often been guided by his heart and while both are well intentioned, both are missing a piece of their puzzle. Slowly though Brennan and Jack are coming to a place of balance between logic and love with the help of their partners, and when they reach their destination they might both be surprised at how fulfilling life can become.