I think Takaya-sensei just kinda, changed it. I, personally think a bird is much more interesting than a rooster would be. Besides, a bird symbolises so much in Kurenos past than a rooster does. *SPOILERS, SPOILERS *

Like the fact that when he had the curse, he was more "free" than he was when he lost the curse. Then he had to stay by Akito's side, because he was too kindhearted to leave, so I think it would be way more cool to call him "The bird inside the cage" insted of "The rooster in cage", don't you agree?
Uhm, ^__^'' Anyway, the point is a bird symbolises Kureno better!

In one of the last few books, Shigure said "Some of us are half-baked versions of what we were long ago". He only uses Hatori as the seahorse as an example, but Kureno as a bird instead of a rooster is sort of implied there.

^That's what I was about to say.