What, according to Scout, causes Jem and her to begin "to part company?"
Scout, Jem, and Dill went on their last adventure of the summer together. Dill was about to leave to go back home. Dill and Jem were determined to peek through the windows of the Radley house in hopes of catching a glimpse of Boo. Scout was hesitant, while the boys were determined to go. Jem told Scout that she did not need to come and he informed her of how she was "gettin’ more like a girl every day." Scout reluctantly went along with them. They were discovered by Mr. Radley, who shot his gun into the air. The three children fled, but Jem got stuck in the barbed wire fence. His pants were firmly stuck, so he left them behind.
Later that night, Jem went back to retrieve his pants. Scout begged him not to go. She was worried that Mr. Radley would actually shoot him this time. Jem knew the risks, but he was determined to get his pants back. He thought that Mr. Radley would hand the pants over to Atticus if he did not. Jem could not stand the thought of his father's disappointment in him. He also did not want his father to punish him.
Despite Scout's pleadings, Jem left in the middle of the night to retrieve his pants. She went with him part of the way. Scout, narrating the story, stated how "it was then... that Jem and [her] first began to part company." Previously, she had brief moments when she "did not understand him." This time left her completely puzzled. She did not think that risking injury or death was worth it to avoid their father's disapproval.
Jem was growing up. He was several years older than Scout. They were beginning to grow apart. Their disagreement about Jem going back for his pants also showed their developing differences as individuals. Jem coveted their father's approval. He was willing to risk his life to keep it. Scout, on the other hand, was more cautious about the matter. She was confident that Atticus would still love Jem, even if he did get into trouble.
Simply put, Jem is growing into a teenager. After a while, it's not cool to hang out with your little sister. Also he is also seeing that the world is not the safe place that he thought it was. Scout doesn't have the life experience and cannot understand all the events that happen around her. Jem is beginning to.