Motomiya Daisuke: Daisuke's life seems very simple: his attitude, his line of thinking, his family situation. Daisuke has a sort of innocence about him in that he doesn't dwell much on the future or the past. He's not stupid, but to him, focusing on anything but what's in front of him is pointless. He's rash and stubborn as a result.
These traits tend to make others think of him as an idiot or a jerk. Daisuke doesn't fully understand why, but when they treat him poorly, he does understand that he feels badly, and either lashes out or becomes depressed. For example, if Hikari was to say a harsh word to him, he wallows with depression. But when Jun teases him, he becomes loud and angry, and writes off his sister as 'stupid' or 'a jerk.'
In reality, Daisuke has an inferiority complex. As the youngest child of a household, it is understandable Daisuke would feel underappreciated, his parents are rarely home and his older sister doesn't treat him as if he means anything. While Jun is probably a nice person and loves her brother, she, like most older siblings, would find him annoying and the two wouldn't get along well at this age. Not to the point where Ken was with his brother, Daisuke masks his feelings of inferiority with energetic loudness.
(An interesting parallel of Japanese culture can be seen with Daisuke, Ken, and Miyako; all youngest of their families. Ken has the worst scenario: he's the youngest boy, and so he's passed over for his brother. The outdated primogeniture law, which used to be very prominent in Japan and still affects their way of thinking, states that the oldest male inheirits everything, and so Ken -subconsciously- has no place in a family that has an older male. Daisuke is the youngest child, but he is the oldest male, therefore he still has a purpose in his family. This could explain why Ken's inferiority complex is much more developed than Daisuke's when it comes to their siblings. Miyako is the youngest girl and therefore becomes loud to get attention, as the oldest girls already have a place in the family. Miyako needs the attention just as badly as Ken, but she manages to receive it somewhat, whereas Ken was completely passed over.)
Daisuke looks up to Taichi because of Taichi's outward assuredness. In an attempt to subconsciously feel that self-assured, Daisuke tries to emulate Taichi in every way, making friends with Hikari in the process.
Daisuke's feelings of insecurity are compounded by the sudden introduction of Takeru into his newfound friendship with Hikari. When Daisuke, who was apparently friendless save for the Yagami family, sees his best friend Hikari become less interested to spending time with HIM, he feels hurt and lashes out at Takeru in jealousy. He also becomes instantly competitive with the boy who seems to be taking Hikari's attention away. As I see it, Daisuke doesn't really have romantic feelings for Hikari. More likely, Daisuke was confusing a close (possibly one of his only) friendship with love.
When Daisuke is thrust into the responsibilty of becoming a Chosen Child (and the figurehead leader), he takes it at face value and wants to do a good job, not realizing the complications and responsibilities required of him. For one, he has to win a war, and two, he now has teammates he must look after (though more often they tend to look after him). They ridicule him and he lashes out loudly, not understanding why his friends would treat him poorly. Thus, his initial persona comes off as a jerk, it's really just a defense mechanism.
As the others begin to accept him again, he realizes what real friendship is, and his close friendship with Hikari is seen as just that: friendship, not love. He and Takeru become closer friends as well. Now that he is emboldened by friendship, his feelings of inferiority are lessening and he becomes a brave leader and trusting friend. His simpleness becomes his best quality again, and it is this childlike attitude that draws Ken out of his self-inflicted torture, realizing that Daisuke can forgive anyone who's truly apologetic.
Thus, Daisuke feels inferior because those around him don't understand him and exclude him. Because he has such a simple way-of-thinking, he cannot cope rationally with his feelings as tends to lash out as a defense mechanism or become depressed. His loud and boisterous nature comes from these feelings of insecurity, and when his friends begin to understand him, his simple nature allows him to accept this quickly and become happy and trusting and brave one again.
In Michi E No Armor Shinka, Daisuke trys to change his image. He emulates Yamato, Koushirou, even Ken (Kaiser-Ken, to be exact) with very poor results. Takeru and Ken tell him that they like the simple, non-thinking Daisuke the best.
Takaishi Takeru: Takeru is no longer the bright-eyed, hopeful, little child. He hides his true self behind a false smile and a fisherman's hat. He is now wise enough to understand what is going on around him. Takeru also habors emotional scars from watching Patamon die at the hands of Devimon. So when the Kaiser trys to manipulate the forces of evil, Takeru snaps and physically attacks him. Takeru also shows his hatred of darkness during the Black WarGreymon story arc. This side of Takeru is almost never shown and this violent form even scares Iori, who is almost always calm and fearless.
His parents' divorce has also now visually taken an effect on him. While not as serious as it did Yamato, the damage was still done. As Belial Vamdemon showed, one of Takeru's greatest desires is that his mother and father remarry. He feels like they aren't a family, like Ishida-san isn't really his father, like Yamato isn't his brother. However, Takeru was lucky, feelings like this are the least of what most children of divorced parents feel. Suicide is the other extreme; Yamato's condition was a mid-level effect.
Takeru always keeps his promises, even ones that were made years ago. During the fight with Piemon, Sora made Takeru promise to protect Hikari. 3 years later, this promise is still the driving force of Takeru's life. When Hikari is taken by Dagomon, Takeru goes nuts and desperately searches for her. Later, after he rescues her, Hikari, Miyako, and Ken are pulled into the World of Darkness. Once again, Takeru loses his mind over the his failure to protect Hikari. However, it's not only because of his promise, he also loves her. This is one of Takeru's most painful dilemmas. Should he confess to her? Hikari's friendship means a lot to him, however, he loves her more than a friend. That is his hardest choice, it's a very risky gamble. If he wins, he gains the love of his life, if he fails, not only will he lose Hikari's heart, but also lose her friendship.
Once again, don't flame me. While I am a Takari supporter, my personal preferences don't influence my analyses. This is stated because the series gives plenty of evidence, even without counting the infamous Toei final episode poster. That picture works in my book, they're holding hands. In Japan, intimate physical contact (holding hands, hugs, kisses
Yagami Hikari: Her sibling complex from season 1 still remains. However, she now holds Taichi on an even higher level than she did before. Daisuke is only a figurehead. He really doesn't have any influential power over the rest of the CC. Takeru and Hikari are the unofficial leaders. They are the most experienced and the most battle-hardened. While Iori, Miyako, and Daisuke can't comprehend the idea of killing an opponent. Takeru and Hikari can kill an enemy and not think anything of it. Hikari has the most power in the group. If Takeru comes up with a plan, Daisuke rejects it purely out of jealousy. However, the moment she agrees with Takeru, Daisuke says he loves the idea. So the responsibility of leading the CC falls onto her shoulders.
Hikari fails to successfully lead them in her eyes. She compares her lead to Taichi's. Constantly living in her brother's shadow and always trying to surpass it destroys her mentally. She feels like she will never be as good as her brother. This is prominent episode 13 (written by Chiaki J. Konaka, not Hiroyuki Kakudoh [the usual director]. Konaka likes having beings rise up from the sea [Big O] and usually writes with a very dark theme [Serial Experiments Lain and Tamers], as I'm sure you have noticed by now.), Hikari is depressed because she is being consumed by her brother's accomplishments. She feels like she would never be as good. Taichi dominated her mind, this eventually drove Takeru over the edge and he told her to stop trying to become Taichi and to be herself. However, the way he said it made it sound rude and angry, so Hikari now feels abandoned by her closest friend. While trapped in Dagomon's domain, she realizes that she it's ok to want to be protected by loved ones. She calls out to the three people she loves the most: Taichi, Tailmon, and...Takeru (see notes on Takeru). Even though Tailmon and Takeru rescue her, Hikari is still vulnerable to Dagomon's call*. However, she finally understands what Takeru was trying to tell her and she can always count on him to protect her.
*This is a pun on episode 13's title "Call of the Dagomon".
Hida Iori: Iori's family situation puts him in a position that would lend itself to having deep psychological problems. His father died protecting a high-ranking government official, and his mother has become very hard as a result. Instead of becoming bitter to his mother or to the world for the loss of his father, Iori has been able to overcome these effects with the strength imparted to him by his upbringing by his grandfather. His grandfather has given him peace of mind by explaining to Iori that his father died with honor and glory (taking a bullet for a government official deserves honor and recognition in Japan). Iori's personality mirrors his grandfather's, who is a perfect example of Japan's view of the perfect male: strong, proper, and stern*.
Iori's personality is, as a result, stern. He is very strict in the way he views reality. He dissapproves of idealism, and is a realist. This way of thinking tends to make him judge others on his first impressions, and he realizes how hard it is for a person to change. This lends itself to a very unforgiving personality. His intial reaction to Ken overcoming his Kaizer-self was disbelief, he looked for any reason to denounce Ken's change-of-heart. It wasn't until Ken proved himself time and time again that Iori could accept his change. After the realization that people could change, he began to become less stern, though still a realist at heart. In the battle against BlackWarGreymon, Iori saw that the only way to stop BWG realistically would be to reason with him, and Iori saw that BWG had the potential to change, just like Ken did.
Iori's biggest problem is that he still misses his father, he never got to really meet him, so in his mind, his father was perfect. Iori strives to live up to him, and his biggest wish is for his father to be proud of him. Iori misses his father, but luckily he hasn't been traumatized by it due to his stern upbringing.
*This stereotype has appeared in other anime, Rokumon Tengai Mon Colle Knight for example. In Rokumon Tengai Mon Colle Knight, Tanaka's punishments (despite how comical they are) are designed to make the Count more like a proper Japanese man (ironically, the Count is German).
Inoue Miyako: Miyako comes from a family where she is the youngest of four children (1 older brother and 2 older sisters). As a result, she is affected by an intense sibling rivalry. Her loud, outspoken personality is derived from a need to be recognized. She is drowned out by her elder siblings in her home. So the need to make herself heard carries over to her social life. However, she subconsciously wants it like that. Miyako has developed a habit of it. Despite how she immediately wishes to be an only child, deeper down, she can't live without competing for the spotlight.
Miyako also has a tendency to be mercurial. Her moods tend to change rapidly from one to the other (this is very common in anime females, intended to be an exaggeration of how females can be in real life. However, for the sake of the analysis, these kinds of mood changes will be treated seriously). It's quite possible that Miyako has developed a bipolar personality as a defense mechanism. She feels the need to be able to adjust to any situation to fit in and be heard, and this stems from her need to compete with those around her for attention. For example, when Miyako realized that the team needed to become serious to defeat the Digimon Kaizer, Miyako went overboard and became militaristic to the point that it endangered Hawkmon. As soon as she realized that this was the wrong way to act, she instantly became remorseful and apologetic to the opposite extreme. She also has a tendency to change from her more serious self to a starry-eyed fangirl at the drop of hat.
Miyako is the oldest of the new team of Chosen Children, and is the one with the most amount of 'crushes' throughout the season. However, she is very miffed when she realizes that Hikari has much more luck with males than she does. As a result, she wishes to be more like Hikari, who coincidentally admires Miyako's outgoing persona, and Miyako works herself into a fervor over Hikari's charm. Miyako almost ruins her friendship with Hikari, but managed to talk it out with her. Miyako comes to terms with herself when she realizes that Hikari admires her just as much as she admired Hikari. This allows her to realize her own self-worth as an outgoing, caring person, and her need to be the center of attention lessens a signifigant amount, and Miyako becomes a more content person.
Ichijouji Ken: Ken suffers from many illnesses. They stem from his relationship with his brother Osamu. Osamu was a child genius, so his parents favored him. At first Ken, was happy for his brother. However, Ken's opinion of Osamu changed when his fame as a genius when to his head. Ken was relatively ignored by his parents as all they could think about was their genius son. Meanwhile, Osamu became very cold and sometimes abusive (not as much abusive as cold. Osamu has been shown striking Ken, but that was only once. Don't take it any further than this) towards Ken. When they found Ken's digivice, Osamu assumed it belonged to him. When Ken took it to look at it, Osamu forcefully took it back (This is the previously mentioned blow. I'm sure you all know of Ken and Ryo's adventures in the Digital World together so I'm not going into it). That was when Ken couldn't put up with Osamu anymore. He wished that Osamu would die, and fate being the cruel mistress she is, the next thing Ken knows, Osamu is hit by a car and dies. Ken suffers from guilt, he wished for it to happen after all. So Ken completely changes his lifestyle and devotes his life to his studies to try to earn himself forgiveness. He forces himself to become the genius child that his parents lost.
We all know that Ken has been to the Dark Ocean. This was because of the darkness infesting Ken's soul: his guilt for Osamu's death and the black seed embedded in his neck. His mind was possessed by darkness and he became the Digimon Kaiser, the man we all love and hate. After Chimeramon's defeat (I believe the idea to make him was part of the black seed's influence. Chimeramon is a lower form of Millenniumon), the black seed's control over him was broken. Ken realized what he did, and had a mental breakdown. Wormmon's death didn't help either. That led Ken to an emotional breakdown.
For the rest of the series, Ken will loathe himself and assume everyone else hates him too. This is why he avoided the CC for a while. Even after Iori (the most reluctant of the group) accepted him as a CC, Ken will always hate himself and refuses to forgive himself. This is shown during Belial Vamdemon's illusions. The illusions Belial Vamdemon created were supposed to show the CC one of their greatest desires, fufilled. However, Ken saw himself, dressed as the Kaiser, being ruthlessly beaten and eventually killed by a swarm of vengeful digimon. Death is Ken's greatest wish. He wants to die, he feels that is the only way to atone for his sins. He tortured and slaughtered hundreds, even thousands, of digimon, and in his eyes, he killed his own brother. However, Ken is forced to live with this burden on his back because he knows what would happen if he killed himself. He would abandon Wormmon, all of the rest of his friends, and completely destroy his parents. The Ichijouji family had already suffered from the loss one son, they don't deserve be tortured again by losing their other son. With this knowledge in mind, Ken is forced to continue living with a guilty conscience in his heart and a dark cloud over his head.