What is it about Tom's case that strikes so deeply at what Atticus believes in To Kill a Mockingbird?

Atticus has been forced to defend Tom Robinson; Judge
Taylor had pointed to Atticus and said, "You're it." The judge knows that no other
attorney would defend Tom as strenuously as Atticus. And Atticus knows that Tom deserves
a fair trial, believing him innocent of the charges against raping a white
woman. Atticus knows that it is one assignment that he can not turn down. He worries
that Jem and Scout will become bitter, but more importantly, Atticus is afraid that they
will catch Maycomb's "usual disease"--the racist hatred of the black
man.

Why
reasonable people go stark-raving mad when anything involving a Negro comes
up...

Atticus explains that
he would not be able to "hold my head up in town" if he didn't take the case, and that
he could never expect Jem and Scout to trust him again. Trust--both with the townspeople
and his children--are very important to Atticus. He knows he cannot win the case, but he
must try.