en.wikipedia.org/wiki/Talking_bird

This sentence pairs the common name sulphur-crested cockatoo with the wrong scientific name.

Authoritative bird references identify the sulphur-crested cockatoo as Cacatua galerita, not Cacatua sulphurea. The Australian Museum's species page for the Sulphur-crested Cockatoo lists its scientific name as Cacatua galerita. Meanwhile, the U.S. Fish & Wildlife Service lists Cacatua sulphurea as the yellow-crested cockatoo, which is a different species.

So the article's parenthetical scientific name is incorrect even if the general statement about talking ability is intended for a cockatoo species.

This sentence is contradicted by documented evidence from another bird group.

A 2021 peer-reviewed study in Philosophical Transactions of the Royal Society B reports vocal learning in the Australian musk duck (Biziura lobata), a waterfowl species in the order Anseriformes. The authors state that a hand-reared musk duck imitated "a human voice", and describe this as evidence for advanced vocal learning in a bird outside the songbird/parrot groups. PubMed's abstract for the same paper likewise says the study provides evidence for vocal learning in the Australian musk duck and that a hand-reared individual imitated "a slamming door and a human voice."

Because waterfowl are neither songbirds nor parrots, the article's claim that songbirds and parrots are the two groups able to learn and mimic human speech is incorrect.