You're braver than you believe, and stronger than you seem, and smarter than you think.
— A.A. Milne
One of the quiet or nearly hidden theme of the show was how each main character viewed themselves.
Jack's alleged personality flaw was the lack of leadership skills (the life or death decision making process) instilled in his mind by his aloof father. But that characterization is not seen in any of Jack's background story. From the earliest moments, he stood to a school yard bully for his friend (and paid the price.) He was a emergency room trauma surgeon. He had to make quick decisions, bark out orders, and deal with life or death issues every day. He had to keep his emotions in check. The one critical aspect of his professional practice was that he always gave his patients hope because he could not accept the fact he could not fix everything.
Jack's character was supposed to die early in the series. His death was supposed to "shock" the viewers to the gravity of the island survival. Kate was going to be the focal point character for the series. It is hard to imagine now that Kate would have carried the series. Jack's personality and demographic appeal kept him on the series (the pilot was killed instead.) By Jack staying in the series, it gave the writers the opportunity to "save" injured people, or allow them to die while Jack struggled to cope with their deaths (i.e. Boone).
Kate was never a leader. She was always a runner. She would get into trouble. Her solution was run away, not be accountable or responsible. She was the anti-leader. She was not even a good follower. She was a loner. Loners with serious baggage are quite independent. Kate probably enjoyed her rebel persona.
Sawyer was Kate's kindred soul. He also had serious baggage, including murder, in common with Kate. He was a loner who enjoyed playing with weaker individuals. He was not about gaining power but rigging situations for his own personal benefit. He did not want or need followers or friends. Sawyer learned the con man trade in order to get into the world of Anthony Cooper, the man who destroyed his family and his life. Sawyer thought of himself as a avenger, the only person who could exact closure to his own personal pain.
On the other hand, Locke aggressively sought out friendship and purpose. His parental abandonment left a big hole in his life. He wanted to be wanted; he needed to be needed. Locke turned his back on what he was good at (school, science) to try to be something he was not (a jock). As a result, no one accepted him. He tried too hard to fit in, including joining a commune. But he was so naive, he did not understand that he was constantly used as a pawn in other people's games.
When Locke arrived on the island, he had another opportunity to change his persona. He acted like he was the great outback hunter. He could provide food, shelter and guidance to the survivors. It was hard for him to accept that the beach camp gravitated toward the doctor over his skill set. This drive to be accepted by his peers led Locke to become another pawn in the Island's game.
Then you have a character like Sayid who actually knew who he was: a dark soul soldier. He knew he was brave. He knew his was deadly. He hated himself that he could lie, torture or kill his opponents without guilt or shame. He had the experience to be stronger, smarter and more clever than anyone around him. He should have been a natural born leader, but he allowed himself to follow orders instead of commanding center stage. In some ways, he was anti-Locke, who wanted to give the Braveheart speech and lead the survivors in battle. Sayid was more comfortable doing his solo missions because he never wanted to be responsible for the safety of another person.
Braver. Stronger. Smarter.
Which characters found themselves outside their personal comfort zones during the Island time?
Jack was braver in dealing with human conditions he could not control on the Island. The physical aspects of finding water, keeping people on point, going on missions made him physically stronger. But the added responsibility did not make him any smarter, because he continued to misjudge people and their motivations.
Kate was slightly braver when she went on missions for the sake of a group goal. But she continued to be distant with interpersonal relationships unless it gave her leverage. She was always a tom boy on the run so the island events did not make her physically stronger. She really was not that dependent on the group for survival. Her island time did give her more chances to charm the men around her. She was always street smart and could see through people like Sawyer.
Sawyer became braver when he gunned down a polar bear on the group's first mission to find rescue. He volunteered for a near suicide mission to go off on Michael's raft. It seemed that the Island kept throwing him into dangerous situations where he had to physically fight back. So he became physically stronger, but mentally weaker. He got conned by other people around him, including Ben. But for the time travel tangent with Juliet in Dharmaville, Sawyer would have wound up as an egotistical manipulator like Ben.
Locke never fit in. He appeared braver after the crash, but the group did not accept his bravery (some feared it). He appeared stronger like a survivalist after the crash, but his emotions got the better of him. Emotions that clouded his judgment. Locke fixated on things as the answer to his own problems (and therefore, the answer to everyone else's problems). When he was wrong, it made him more bitter. And the more bitter he got, the weaker people perceived him. He was not very smart because people easily made him the fool. Locke's island tenure mirrored his miserable pre-crash life.
Sayid's time on the island was also a non-change. Sayid was always a brave soldier, always able to do the group's "dirty work." He was stronger than anyone around him. He was military smart in tactics, weapons, killing and gathering intelligence. As such, Sayid was viewed by those in power as tool to be used to secure or maintain power. First, Sayid worked for Jack taking the dangerous missions in the jungle. Then he worked for Ben as an asssassin. Finally, he worked for MIB on the island. Once Sayid was killed and reincarnated in the temple, Zombie Sayid finally realized that he was an empty shell. He was no longer independent, but a pawn who did not think much of himself.
Clearly, all the main characters went through a lot of trials and torment on the Island. But did they really change that much? Did a light bulb go off and suddenly make them smarter? Did a dormant trait hidden deep inside them awaken to make them stronger? Did their fits of bravery more heavily rely on basic instincts over courage? It may be subjective to answer those questions. It depends upon how you viewed each character's life before and after their Island time periods. But it is interesting to note that none of the main characters came to the self realization that they truly changed as the series closed. Kate continued to run away. Sawyer was self-motivated to get off the island. Locke and Sayid died in meaningless ways. And Jack never came to grip with his emotional demons. No one came out and said that they had an epiphany; that they were a changed person.