This question is a bit vague and subject to interpretation. Nonetheless, it seems like the question focuses on the color symbolism of both the cap and the red hair. The cap, being black, may symbolize death or evil, and his red hair may symbolize hatred. One could build a case for this answer if you talk about the qualities of Jack--how he ultimately brings death to the island through the killing of pigs as well as Piggy and Simon. The symbolism of his red hair could be supported by his personality and his "blood lust" for hunting and killing.
Hope that helps...
The teacher who commented on this left out the fact that these caps are a symbol of the boys' descent into savagery. Each time Golding mentions them, they have deteriorated. In chapter one, the caps are addressed as "square" and black (Golding 19). Further along in the novel, the boys are seen as nearly naked yet still wearing the REMAINS of a black cap. This word "remains" is obviously quite important. In the very last chapter Jack is described as wearing the "remains of an extraordinary black cap" (201). "Remains" are just a fragment, just a trace of what once was. The boys, who come to be called "savages" (with good reason) have only remains of their past CIVILIZED lives. This is seen in very small, seemingly inconsequential quotes such as "[Jack and Ralph were] unnerved by each other's ferocity." (179)