Your question asks why Pecola from The Bluest Eye can be viewed as a victim of her family, society, and American racism. After reading the novel you probably realize that the situations in the novel are based upon the racism faced by African Americans in America. It is the history of discrimination that serves as the general cause of the difficulties Morrison's characters face.
Pecola's parents mistreat her because she is the image of everything they hate about themselves. Portrayed in the novel as immersed in self-hatred, Pauline and Cholly first grow apart from each other and then from their children. Pauline's contempt is illustrated by the way she ignores Pecola in preference for the white child she is paid to mother and the white family she is employed to serve. Cholly's abuse of Pecola is physical and violent. In a drunken haze, Cholly sees his daughter as a replica of her mother who he once loved.
The society abuses Pecola like a bully on a playground. It seems that each person who lashes out at her is full of his or her own anger and hatred. Unable to change their own status in life, they all attacked the one who is weaker. The white boys throw rocks because as male children they have limits on how they behave from parents, elders, teachers, etc. However, with Pecola they have no limits. She is black, so they view themselves as simply better than her because they are white. The members of the segregated black area of town also abuse Pecola because of her dark skin and family dysfunction. One boy called Junior lures Pecola into his house.
Once there, Junior, who is jealous of his mother’s blue-eyed, black cat, throws the cat in Pecola’s face and locks her in the room. When Junior discovers that Pecola likes the cat, he hurls the cat against the wall, leaving it unconscious. (eNotes)
Junior abuses Pecola and the cat because they are both black, which is something he hates. In addition,
Pecola’s pregnancy at the hands of her father causes a terrible scandal, and Pecola is thrown out of school. The town condemns Cholly but feels that Pecola must share some of the blame for not fighting back. (eNotes)
Overall, the characters in the neighborhood cast out the Breedloves because they know that blacks are viewed as one entity; if one black person steals, then whites view all blacks as thieves. If a black father rapes his daughter, then all black fathers will be viewed as incestuous rapists.
Understanding how Pecola is a victim of American racism requires having a clear understanding of color consciousness in the African American community. Pauline, Cholly, and Pecola are all dark-skinned. "In America, skin color is an important signifier of beauty and social status" (Race, Racism, and the Law). The Breedloves hate their black skin and blame it for the condition of their lives.
African-Americans' preference for light complexions and European features dates back to the antebellum era when skin color determined an enslaved person's work assignments. Dark-skinned slaves worked in the fields, while light-complexioned slaves worked in the slave owner's home. (Race, Racism, and the Law)
The difference in treatment created a hatred-driven rivalry between the two groups of slaves, a rivalry that to some extent remains in the African American community since light-skinned blacks still find it easier to exist in a culture historically defined as white. In Morrison's novel,
Pecola's predicament was caused by internalized attitudes about what was considered attractive and desirable in her immediate reality. (Race, Racism, and the Law)