Under the Jim Crow Laws of the setting of To Kill a Mockingbird, the destiny of African-Americans was controlled by whites. Therefore, after having been convicted of a crime by an all-white jury when there was clear evidence that proved that he was innocent, Tom has no faith in the legal system and feels that he has little to no chance of acquittal in an appeal case. For this reason, he attempts escape as the only way he can possibly live.
In Chapter 21, after having listened to the false charges and perjured testimony of Bob Ewell and his daughter Mayella, the Reverend Sykes observes that Judge Taylor was very "fair-minded" as he charged the jurors before they retired to the jury room:
"He sorta said if you believe this, then you'll have to return one verdict, but if you believe that, you'll have to return another one. I thought he was leanin 'a little to our side--"
Jem assures the Reverend, saying that he cannot understand how any jury could convict Tom with all the evidence to the contrary, but the minister interrupts him, "I ain't ever seen any jury decide in favor of a colored man over a white man...." as he understands the system under which his people live with the Jim Crow laws.