Jem saw through the injustice and the racism of Maycomb. When he talked to Atticus about it and Atticus tried to explain to Jem the judicial process, Jem was still upset.
In particular, Jem was upset that the jury had so much power. This is why he wanted to do away with the jury. He realized that the ordinary citizen of Maycomb was unreliable when it came to the color of a person's skin. Here is what Jem says:
“Then it all goes back to the jury, then. We oughta do away with juries.” Jem was adamant.
Atticus at that point tried to explain to Jem that there are good people out there. This means juries could be fair. Atticus, therefore, gives an example by saying if the jury was made up of boys like Jem, Tom would have won the trial. Here is what Atticus says:
“If you had been on that jury, son, and eleven other boys like you, Tom would be a free man,” said Atticus. “So far nothing in your life has interfered with your reasoning process. Those are twelve reasonable men in everyday life, Tom’s jury, but you saw something come between them and reason.
Jem was still upset. What made him really upset was the reality of Atticus' words, that a white man's word will always beat a black man's word. Atticus said:
In our courts, when it’s a white man’s word against a black man’s, the white man always wins. They’re ugly, but those are the facts of life.”