This is an interesting perspective on this short story. "The Sky is Gray," by Ernest J. Gaines, is set in the South (Louisiana) during the 1940s. This is a time and place in which both racism and poverty flourish, and James and his family certainly experience both.
Your assessment of the problem is that black people are passive because of tradition or some other factor but that this boy is an exception as he is active on the inside. Perhaps there is another way to look at what you call "passive" and "active." There is an inherent pride in James and his mother, typical of many black people in their circumstances. They understand they are seen as a lower class of people in society, and they have to do what they can to maintain their dignity in the face of that overwhelming condemnation. What you see may appear passive; however, what is happening on the inside, the undercurrent, is maintaining a sense of pride and self-sufficiency in order to combat the prejudices surrounding them on the outside.
One good example of this happens in the waiting room of the dentist. After waiting for a long time already (because he is the cheapest dentist and many people are there), the nurse disdainfully announces to the crowd that the dentist will not see anyone else until 1:00. They need to leave and they do, which can seem like passivity--simply accepting what others tell them to do. But Octavia and James do not simply stand outside the door and wait. Instead, they walk. It is bitterly cold, and Octavia knows James is suffering. Instead of simply ignoring the fact or asking for permission to get warm somewhere (which may or may not have been granted them), she takes them to a hardware store. Octavia asks to see some merchandise, giving her son time to warm himself. A passive woman would simply have hoped for a place to warm up; a proud woman needs to feel as if she is not taking a handout while still providing for her son.
So, while they may look passive, there is plenty going on inside both James and Octavia. She is determined to provide the best she can for her son in these difficult circumstances. He understands his mother is trying to make him self-sufficient and strong so he, too, can face what is ahead of him--which is why she makes him kill the bird. In general terms, this is not an uncommon way of thinking for any oppressed group of people. Even though others may not see value in them, they have pride enough to see value in themselves; and, despite the obstacles, they are determined to do what it takes to survive with their self-respect and dignity intact.
In terms of writing a paper, it might be interesting to approach this idea of inherent pride which only appears to be passivity. You can find this theme in many other works, as well, including Eudora Welty's "A Worn Path." I've included a great eNotes link to that story below. Best of luck in your writing!