Atticus is one of the most fair-minded, kind-hearted, morally-motivated men in the entire city of Maycomb. Think of all of the examples that prove he is a defender of equality and justice. He doesn't tell anyone that he is an excellent shot with a gun, because he doesn't want to brag about his talent, and doesn't want anyone else feeling poorly because they can't shoot as well. He has a black woman working for him that he pretty much taught to read, and treats as a total equal, and has let raise his children. He is an advocate for Boo Radley, telling his kids to leave the poor man alone and let him live his life, even if it is a bit of a strange way to live it. He gives Scout the low-down on how she must attend school because it is the right thing to do, and that she must be kind and not fight with other kids who are taunting her. He teaches Jem a valuable lesson about kindness and courage in the situation with Mrs. Dubose; Atticus even called her brave, even though she was a mean woman who constantly insulted him.
All of these examples show how Atticus was the right man to defend Tom Robinson in a case that was probably a hopeless one from the start. He believed, more than anyone, that Tom deserved the most fair trial that he could have. He believed that he wouldn't be able to look himself in the mirror every morning if he didn't do the right thing. He knew the town inside-out, knew its people, and knew the best way to argue the case. He believed in justice and equality enough to take the case, where others might have turned it down, and he stuck with it until the end, even though he suspected he would lose. All of these reasons and more are why Atticus was the perfect man for the case, and Harper Lee spends much of the novel developing his character so that we actually believe he is the man for the job.