What is meant by Scout's comment from To Kill a Mockingbird, "It was then, I suppose, that Jem and I first started to part company"?
Scout realizes that her brother is looking at the world from a more adult perspective.
Atticus had been telling Scout and Jem to leave Boo Radley alone for a long time. They had mostly ignored his orders, because they were intent on making their reclusive neighbor come out. Their friend Dill in particular believed that if Boo just sat on the porch with them for ice cream, all would be fine.
Things get particularly bad one night when Jem, Dill, and Scout are trying to get a look at Boo Radley and Jem ends up losing his pants. The children explain their absence to the adults by telling them they were playing strip poker. The problem is they still don't have the pants.
When Jem tells Scout that he is going back to get his pants so that Atticus will not know what really happened, she panics. She is afraid that Nathan Radley will think that he is a prowler and shoot him. No pants are worth that.
He blew out his breath patiently. “I—it’s like this, Scout,” he muttered. “Atticus ain’t ever whipped me since I can remember. I wanta keep it that way.”
... “You mean he’s never caught you at anything.”
“Maybe so, but—I just wanta keep it that way, Scout. We shouldn’a done that tonight, Scout.” (Ch. 6)
Jem means that they should not have disobeyed Atticus. He is starting to understand the importance of integrity. Lying about the poker is about to catch up with him, and he can't bear for Atticus to find out the truth and be disappointed in him.
Scout doesn’t understand why it is so important to Jem to go back and get the pants. She tells him, “It’s not like he’d never speak to you again or somethin‘…” For Jem, it is about the loss of respect. Scout is still looking at the world from a child’s perspective, but Jem is starting to think like an adult. That is why she doesn’t understand him. The difference in years between them is showing.
Jem goes back for his pants, and finds them sitting on the fence. They have been sewn, inexpertly. Boo Radley wanted to make sure that Jem found them and tried to prevent Jem from getting in trouble. Jem didn’t completely understand all of that at the time, and the pants’ presence mystified and disturbed him a little. The incident demonstrates how involved Boo Radley is in the children’s lives. He is already a inextricable presence, very aware of everything that is going on in their lives, even before they know it.