This one is fairly easy for me ^^ In his canon, at one point, Fai is given control of a Kudan, which is a sort of... god that bonds with each person in that world. IT'S REALLY WEIRD, but the point is, they sort of represent what kind of person you are the way a daemon does. Add that to all the 184738947582 times Fai is shown with bird/phoenix imagery, and the fact that the TRC group are obviously supposed to represent four elements (Fai = Wind, Kurogane = Ice/Water, Syaoran = Fire, OTHER Syaoran = Lightning, Sakura = Earth)... well, there it goes. Also he would probably jive well with the witches.

But since his Kudan is FREAKING HOUSE SIZED and phoenixes aren't an actual thing, I decided on a Nicobar Pigeon. This, this, this and this should tell you all about why. They're just that fabulous. Also, pigeons are clever and social birds, and I bet she'd be a lot more sensible than her human B|