"The Kitten" is actually an episode from Richard Wright's childhood. In his book, he gives an account of what happened when he and his brother discovered a stray kitten wandering near their tenement apartment.

Accordingly, Richard and his brother fed the hungry kitten and gave it water. However, it continued to meow pitifully. Its incessant meowing woke up Richard's father, who ordered the boys to drive the kitten away. However, despite their best efforts, the boys failed to get the kitten to leave. In anger, Richard's father ordered the boys to do everything they could to get rid of the kitten. He even went so far as to suggest that they should kill the kitten if they had to. Of course, Richard's father spoke in anger.

For his part, Richard so resented his father's bullying ways that he resolved to kill the kitten. In Richard's mind, he was paying his father back for all of the times the latter abused him. Essentially, Richard decided that he would take his father's words literally and administer his own brand of cruelty on another defenseless creature.

So, Richard found a rope and literally strung the kitten up until it died a gasping, miserable death. Meanwhile, Richard's brother was horrified at what Richard had done. Frightened and confused, the younger boy told their mother what had transpired. Of course, Richard's mother was furious. When Richard's father discovered what Richard had done, he was also extremely angry. However, he couldn't trash Richard for killing the kitten.

Richard had managed to deceive his father into thinking that he had sincerely followed his orders. So, Richard's father could not punish Richard without risking his credibility and his authority. In this way, Richard managed to avoid a whipping from his father. At the time, he felt that deception was the only way he could retaliate against his father's cruelty.

Richard's mother was not so easily convinced, however. She administered her own brand of punishment on Richard. When night dawned, she ordered Richard to dig a grave for the kitten and bury the dead animal. Richard was horrified. However, his mother insisted. She also led him to think that he would be condemned by God for his terrible actions.

So, Richard was forced to take the kitten down and to bury it by himself. Despite his begging, his mother would not help him with his task. When Richard finished, she led him in a prayer of contrition and even hinted that his life could be forfeit as punishment for his actions. Richard relates that he went to bed in a sorry state that night and hoped that he would never see another kitten again.

I had a hard time finding a summary of "The Kitten", by Richard Wright.  The first link I've provided you with has a short summary.  In order to find it, you'll need to scroll down a bit.  It is under "Part One: Issues of the Family", near the end of that section.  It also gives a very brief analysis.  I hope it helps!  I have also included the enotes section on both Richard Wright and his novel Black Boy, which is where "The Kitten" was taken from, if I'm not mistaken. That may help you to find answers to any questions that may arise, as well.