Parrots can't talk
Not sure what your criteria for "talking" are but, by all of my own measures, my parrot sounds pretty much exactly like me in most cases, and like a child in most others. The words are clearly distinguishable, understandable, and in multiple languages (he lives in a multi-language household).
So, yes. Parrots can talk. Can they converse? Sometimes loosely, usually not at all. But they can very much talk.
If you mean that parrots do not understand the words and construction they are speaking, sure. But at that point you're splitting hairs. My parrot says "do you want it?" when he wants a treat. He says "good night" when he wants to go to bed. He says "c'mon!" when he wants me to come to him. He absolutely talks.
Weird hill to die on.
...but at the end of the day, speech is in many ways "just" a series of correct sounds at correct times in correct situations, right? Does my parrot have a conversation with me? Well yes, sometimes, but not with words. Does my parrot mimic human words and phrases? Also yes, and sometimes in the most perfect situations possible.
I love these little tyrants.
Some have shown the ability to communicate abstract thoughts and feelings.
Why do you say they can't talk?
Noam Chomsky on Nim Chimpsky and the Emergence of Language: https://www.youtube.com/watch?v=a39vcatTCVU
Chomsky has a few other interviews where he addresses this.
In other words a baby saying “milk” because it wants milk doesn’t mean you should ignore it because it isn’t using a “language.”
Ok. Hi cat. Do you need language to communicate? Plz respond.
I owned a parrot for a few years. The speech she had was like a tape recorder, she could mostly only play back what she heard in an identical manner. But she was able to play back pieces of appropriate snippets in the right context to express herself to a level that I'd call it talking. It's not normal "speech", but if you gave an otherwise normal human with damaged speech centers in their brain a tape recorder it's very much like that.
We really need to be aware of our own biases and biological limitations if we actually want to study and understand the ability of other animals to have complex communications. Birds experience reality differently than we do - they see more of visible spectrum, they can make multiple sounds at once, etc. I wouldn't be surprised that what they can hear and how they perceive things like time is very different then us. Anyone observing parrots, crows, and other highly social avians can see they have complex relationships.