SDSTAFF Doug replies:
Probably for the same reason that applies to most things in biology: SEX! [No, apparently not - read on..]
Mynahs, mockingbirds, and various other birds will mimic sounds in their environment to boost their song repertoire. The more complex a male's repertoire, the more impressive he will seem to females (though this doesn't seem to apply to humans, if Michael Bolton is any indication). The idea is that only a superior male, with all his senses in fine form, could learn, remember, and reproduce a wide variety of sounds--so a versatile male should have a higher probability of having "good genes." In practice, it probably just helps weed out the truly inferior males. I suspect your parrot falls into the same class of critters, though it could certainly be disproved easily-- like if female parrots were just as good at mimicry as males. Then we'd need another hypothesis, like improved pair bonding when members of a mated pair imitate one another. Whatever the truth is, the roots of parrot behavior should relate to their behavior in nature, not the artificial environment we put them in.
Hoping to narrow the possibilities a bit, I called a local pet store owner, who informed me there was no noticeable difference between the vocabularies of male and female parrots. That suggests that mimicry in parrots is more of a "social bonding" thing (they do form very tight monogamous relationships, as well as often associating in large groups) than just an "impress the female" thing, as with songbirds.
Still, the claim that the investment of time and energy pays off in reproductive success is still valid, even if it is only a matter of pair-bonding. The term "survival of the fittest" has two components--survival, which is obvious, and "fitness," which is how many offspring you leave behind relative to everyone else. Most everything an animal does relates to one of these. A parrot that mimics sounds may not improve its survival any, but if it leads to more effective communication with its mate, or increased fidelity, then it might affect how many offspring it has and how long they survive.
