I would guess it has to do with complex vocalizations and verbal language being of more importance to birds than most monkeys perhaps? Parrots and corvidaes (crows and jays) learn to understand and speak human words as an attempt to "fit in" and communicate with their group (in captivity that would be us). In the wild, they speak with the chirps and calls that other parrots and corvidaes make. For example, there is a type of parrot that gives a unique chirp to each of its children to refer to them like a name[1]. Crows and parrots can be miles apart at times so that's my guess for verbal language being of more importance to them than other forms of communication. They also have a dialect they speak when near each other and then the more common calls most of us hear when they're farther apart[2].
I know much more about birds than primates, so correct me if I'm wrong. Birds tend to be around people in captivity much more than monkeys, so guessing that may be part of the reason as well.
