First time I've ever posted in the theorizing section. With all the questions of what the relationship between Fi and Girahim really entails, I thought this might help.. probably not
After people mentioning the similarities in the roles of Fi and Girahim to their respective masters, and the fact that Fi is basically emotionless, it led me to make the connection between Fi and Lieutenant Commander Data from Star Trek: Next Generation
Data's creator Doctor Soong, created the android Data, which was meant to "perfect his design of his androids" (quote from Memory Alpha, a Star Trek wiki). However, as revealed by the episodes in the series, Data had a "brother" android: Lore
Off the bat, notice the most intriguing difference, rather the only visible difference, between the two androids: Lore is smiling
According to the same wiki as cited earlier, "Lore was extremely advanced and sentient, possessing superior strength, speed and intelligence when compared to a Human. Lore's emotional programming was also very advanced; however, he began displaying signs of emotional instability and malevolence, leading him to see himself as superior to Humans. Lore frightened the other colonists, who demanded that Soong deactivate him. Lore later claimed that they saw him as 'too perfect' and were envious."
This now brings us to the topic of the two "swords" of the game: Fi and Girahim.
Right off the bat, once again, a huge difference between the two characters is the fact that Girahim is smiling... Something Fi never exhibited.
Fi always mentions the flaws in humans, such as oral communication being so unreliable. Often times, Data does the same throughout the series, pointing out the flaws of the human condition.
However, I think through the last scene of Fi in Skyward Sword we see her almost strive to be human, although it is difficult. She thanks Link, mentioning that it is a part of human tradition. Data throughout the whole series strives to be human, as shown by his attempts at making music, whistling, etc.
Girahim is very similar to Lore as both appear emotionally unstable. Both have emotion, but they don't really know how to control it well.
According to the Star Trek wiki, Lore was created before Data, but Data was created so that "when Data was perfected, his improvements [would be applied] to Lore." (Memory Alpha, Star Trek wiki)
So... Maybe the same could possibly said about Hylia?
She created Girahim at first, but found that he was emotionally unstable, and thus abandoned him like Lore was abandoned by his creator?
Demise took Girahim as his own, with the power to give him a truly human form (the form in the picture of him above)?
Demise used Girahim against Hylia when they fought, but Hylia won, and Girahim disappeared like he did at the end of
SS?
Hylia then created Fi, making her emotionless knowing that emotion would corrupt Fi?
This is all speculation, but it also kind of brings about the similarities between the Lore and Data relationship and the Fi and Girahim relationship.
Just some thoughts.Might shed light on Girahim and Fi's relaitonship. Aonuma might be a big Star Trek fan? (Raises flame shield)