In Traz's case, I guess it's your typical oedipal anxiety. By the time Rhue reaches Lide he has begun to come into adulthood after having sifted through the feelings aroused by his, "awakening," of sexuality during his encounter with Lyrra. This experience is reinforced further when he meets Cetsa and contests(though in a friendly manner) with Traz for her attentions. Inevitably, Rhue's rapid maturation becomes threatening to Traziun, who as a result seeks to improve his own masculine prowess, that is to say, obtain a better sword.
Cetsa and Scatha are seeking the shadow sword in hopes salving a deep disappointment in the male sex. Scatha herself never really having known her father and then abandoned in a moment of profound need by her first love while Cetsa quite likely was the target of paternal abuse(haven't finished e5 yet). Each woman has therefore lacked due attention from a strong, positive male influence at an early age and has as a result lost faith in men altogether. Each, therefore, desires to obtain her own, "sword." That is, in other words, to eliminate the need for the opposite sex. Given the afforementioned feminine trait of questing for a, "perfect," love, each wants to acquire the biggest, badest sword available. Their resultant conflict is a natural outcome.
Kygar is obviously the victim of an unrequited love for Cetsa. When he discovers Cetsa's fascination with the shadow sword-a symbol of a nonpareil masculine power- he seeks to become the strong, perfect love that she desires by , "giving," her the, "sword."
I hope that is something like what Cocoa intended when he wrote these games. It's what I saw, at least.
Seriously, though, some of this stuff actually sounds credible. This is fun.
