Scout and Jem are depicted throughout the book as being fundamentally very close, but they have differing temperaments. Scout is rather hotheaded and quick to act whereas Jem tends to think and reason more. But the difference between them can also be accounted for in terms of age. Jem is four years older than Scout and this becomes significant. He is entering adolescence while she is still very much a child.
The first time that Scout really becomes aware of this gap between them is when Jem declares he's going to fetch his pants, which were caught on the Radley fence. Scout is aghast with terror at the very thought, as it's the middle of the night and the Radley house is the one spot above all others that she fears. She pleads with Jem not to go but he simply won't listen, because he is more concerned at the prospect of getting a whipping from his father for disobedience than with meeting the phantom Boo Radley. Looking back, the adult Scout realizes that this incident marked an important point in their brother-and-sister relationship.
It was then, I suppose, that Jem and I first began to part company. Sometimes I did not understand him, but my periods of bewilderment were short-lived. This was beyond me. (chapter 6)
At the time, Scout is too young to appreciate the fact that Jem is now maturing; he is beginning to leave behind their childhood world of games and childhood fears, and to develop a sense of adult responsibility. The terror of the phantom Boo Radley, who has so often provided the subject for their childish dramas, is beginning to disperse for him.