Why did Judge Taylor appoint Atticus to Tom's case?

Judge Taylor appoints Atticus Finch to Tom Robinson's case because Taylor believes that Atticus is the only attorney who could give Tom's story a chance to be heard in court in a way that would prevent people from automatically dismissing it.

Scout realizes this in Chapter Twenty-Two after Tom has been found guilty of the rape of Mayella Ewell, despite being innocent. When the children go to Miss Maudie to talk about what has transpired...

Judge Taylor appoints Atticus Finch to Tom Robinson's case because Taylor believes that Atticus is the only attorney who could give Tom's story a chance to be heard in court in a way that would prevent people from automatically dismissing it.

Scout realizes this in Chapter Twenty-Two after Tom has been found guilty of the rape of Mayella Ewell, despite being innocent. When the children go to Miss Maudie to talk about what has transpired in the courthouse, Miss Maudie points out that Taylor had selected Atticus instead of Maxwell Green, who has less experience and talent. This leads Scout to realize that Atticus was chosen because Taylor wanted Tom to have as fair of a trial as he could in the deeply racist town of Maycomb.

Later, in Chapter Twenty-Five, Miss Maudie and Aunt Alexandra discuss the toll that the case has had on Atticus's health, and Miss Maudie comments quite profoundly about Atticus's appointment:

Whether Maycomb knows it or not, we're paying the highest tribute we can pay a man. We trust him to do right. It's that simple.