A fable is a story that involves animals with human characteristics such as the ability to talk, show human emotion and make reasoned decisions, like Schwartz does in "Jewbird" by Bernard Malamud. It is allegorical and provides a moral lesson that has the capacity to reach many people without directly passing judgment on them in the hope that they apply their renewed understanding of a situation to their lives. A fable does have a specific reference point (in this case the life of a Jewish-American family) but can be universally applied to many situations.
The story was first published in The Reporter in 1963, and tells the story of a talking bird who comes to an unfortunate end despite the potential for it to live happily in the Cohen household. Harry Cohen is cynical and his contempt for the bird is apparent. He is more surprised that the bird is a victim of "anti Semeets" than he is at the bird's ability to talk. The story comes to an unnecessarily tragic end which emphasizes the breakdown in communication that occurs between people, making it that much harder for "outsiders" to integrate into a seemingly different culture or society.
Therefore, the story could be considered a fable because it does serve as a warning that there are people who deny or fight against their own heritage or culture, and in doing so exhibit the worst kind of prejudice. Harry Cohen is a Jew himself but denies Schwartz, the "Jewbird," the basic comforts he craves, even though Schwartz tries to humbly accept whatever kindness the family might show him and tries not to be overly demanding. He is displaced, has nowhere to go, but is unable to penetrate Cohen's harsh exterior. Schwartz looks like a bird—a crow—and Cohen refuses to see beyond that even though Schwartz can recite Jewish prayers and reveals his own Jewishness.
A parable is similar to a fable but has a spiritual lesson. Cohen has the opportunity to help Schwartz but refuses to accept that he is anything like Schwartz because it may reveal a weakness or a vulnerability that Cohen is not prepared to face. In terms of parables, he is turning his back on his own people (metaphorically) in the same way Peter denies Jesus in the New Testament. Therefore, Jewbird could also be considered a parable as it intends to teach a spiritual lesson far beyond its immediate scope. The parallels to the story of Peter's denial of Jesus serve as a lesson to others to be strong and have faith. It seems that Cohen has effectively denied his faith.