Atticus understands that winning the Tom Robinson case is virtually impossible due to the systemic racism and prejudice that is prevalent throughout Maycomb, Alabama. In Chapter 9, Scout asks her father if he has a chance of winning the case, and Atticus says, "No, honey" (Lee 48). Scout then asks her father why he is even trying, and Atticus says, "Simply because we were licked a hundred years before we started is no reason for us not to try to win" (Lee 48). Later on, Uncle Jack asks Atticus if he has a chance of winning the case, and Atticus says,
"It couldn’t be worse, Jack. The only thing we’ve got is a black man’s word against the Ewells’. The evidence boils down to you-did—I-didn’t. The jury couldn’t possibly be expected to take Tom Robinson’s word against the Ewells'" (Lee 55).
Atticus realizes that the jury will not accept Tom's testimony as truth for the simple fact that Tom is an African American. In 1930s Alabama, segregation was commonplace, and Jim Crow laws were enacted to separate and discriminate against black people. The Post-Reconstruction era promoted systemic racism throughout the South and Atticus is essentially challenging the entire culture by defending a black man. The jury could not possibly rule in favor of Tom and subject themselves to the cultural taboo of favoring "Negroes."
Atticus mentions to Jim and Scout that the case is sensitive and the whole world is basically against them from the beginning because it's one black man's word against several white people. No matter how upstanding the black man or how unappealing the white people, the whites will always be listened to before the black man's word is considered. Atticus tells Jim and Scout that he isn't just defending Tom Robinson: he's fighting 100 years of history and he is not going to win against all that precedence, no matter how great an attorney he may be.