While I would never say that they are like the yin and yang of each other, but it is possible that they are of similar creation. I would imagine that both were created by the Goddess, but, like some of the other creations, his ill will upon the other beings led him astray and into the hands of Demise.
I have a similar train of thought concerning this sort of situation as I do
the Guardians of the Silent Realm. By this, I mean that the species of Fi and Ghirahim were also involved in the war between Hylia and Demise - be it on Hylia's side, or Demise's. It's very possible that Fi was the only one on Hylia's side, or Ghirahim being the sole being of his people on Demise's side.
This would imply that the other members of this race died during the war. Ghirahim - Demise's trusty sword - and Fi - Hylia's prophet - were the sole survivors of a race that was no doubt created to complement her soldiers. This race was created to be weapons, yet have personalities. Whether this could be in order to create a bond between the weapon and wielder, or for giving the wielder guidance, I can only assume.
Naturally, the only member of this race on Demise's side - or the most powerful that was on the Demon Horde's side - would act as Demise's weapon. Although not seen as such until fought against Fi, Ghirahim later becomes the anti-Master Sword.
Like a few people before myself have said, it is quite possible that we've seen this "anti-Master Sword" already - the Trident of Power. I can only assume that these species reflect upon what the wielder desires. Link desired a pure weapon, and Fi accommodated to it. Demise wanted a dark, intimidating-looking weapon, and Ghirahim too adapted to his Master's wishes. It's quite possible that a trident was what Ganon felt suited him, so his weapon reflected upon what his Master wanted - much like the Triforce.
I think there's a lot of unspoken history between Fi and Ghirahim. Unfortunately, a lot of it will always be left to speculation, and we can never quite know for sure. It's interesting to imagine that the last surviving members of a race were forced to fight the other to the death. And yet, it's just as interesting as it is sad.
