I'm not sure in this drama how far back Brother Liu met Si Feng. It's told that most of then are 6 feathered garuda, so Si Feng is special. Kind of like 9 tail fox, where most of then rarely have 9 tails. The story of phoenix is that not all the bird will become a phoenix, also making the phoenix special? I guess it's to bring out Si Feng being special. Another thing is his name Si 'Feng.', Feng is a part of 凤凰, the full word for Phoenix.
Brother Liu knew Si Feng from when he was very young, so calling him little Phoenix I guess is not too much to think into.