Cannibalism is when you eat your own species. Chickens and parrots diverged about 100 million years ago [1] whereas the common ancestor of all living placental mammals, from whales to humans, lived around 64 million years ago [2]. So for us to be eating any other placental mammal is more like cannibalism than a parrot eating chicken.
[1]
https://content.ucpress.edu/chapters/9930.ch01.pdf[2]
http://science.sciencemag.org/content/339/6120/662