This is a good question. Scout was not always empathetic in the novel. In fact, it was just the opposite. At first, she had no clue about empathy. We see this in two clear examples. First, she beats up Walter Cunningham in the beginning of the book for what readers might think is not a particularly good reason. And when he comes over for a meal, she mocks him for his eating habits.
Second, she thinks of the wildest stories of Boo Radley with no thought of how Boo might think. She, like Jem, views Boo as a nightmarish figure.
Jem gave a reasonable description of Boo: Boo was about six-and-a-half feet tall, judging from his tracks; he dined on raw squirrels and any cats he could catch, that’s why his hands were bloodstained—if you ate an animal raw, you could never wash the blood off.
At the end of the book, she does learn empathy, because Atticus teaches her to walk in another person's shoes. In other words, Atticus wants her to see life from the perspective of others. Miss Maudie and Calpurnia also help her. But most of all, sitting in the trial of Tom Robinson helps her. She see the injustices that Tom has to endure. So, by the end of the book, she is very empathic. This dialogue says it all:
Atticus sat looking at the floor for a long time. Finally he raised his head. “Scout,” he said, “Mr. Ewell fell on his knife. Can you possibly understand?"
Atticus looked like he needed cheering up. I ran to him and hugged him and kissed him with all my might. “Yes sir, I understand,” I reassured him. “Mr. Tate was right."
Atticus disengaged himself and looked at me. “What do you mean?” “Well, it’d be sort of like shootin‘ a mockingbird, wouldn’t it?”