We are not supposed to say anything new, because everything that needs to be said has already been said by our Poorvacharyas. It is our duty to follow their teachings just like a parrot repeats what is said to it. Even though a cuckoo sings beautifully as Andal sings HER pasurams, it does so on its own free will and not as told. Hence a parrot and not a cuckoo or any other animal or bird is chosen as an example for all Sri Vaishnavites.
Even Andal HERSELF was represented as a parrot in several instances by Pillai Lokam Jiyar in his “thaniyan vyakyanam” for Naachiyaar Thirumozhi.
“ANDAL who is the divine parrot that was born and brought up in the gardens of vishNu cittar”. It is interesting to note that piLLai lOkam jIyar in his “taniyan vyAkyAnam” for nAcciyAr tirumozhi tries to establish kOdai as a kiLi (parrot) in many ways: “periyAzhvAr tirumagaLennum madippuDaiya kiLi” - the parrot who had the honor of being periyAzhvAr's esteemed daughter; “AzhvAr ASramattil kiLi” - a parrot in AzhvAr's ASramam; “periyAzhvAr tEnum pAlum amudumAya tirumAl tirunAmattAlE vaLarttu eDutta kiLi” - the kiLi who was brought up by periyAzhvAr with the Lord's tirunAmam which is sweet like honey, milk and nectar; “vaLarttu eDuppArkkum kAlilE vaNa’nga vENdum paDiyAna kiLi” - the kiLi, who exceeded Her father and thus became even worthy of worship by him (by becoming the Lord's consort).