In Harper Lee's To Kill a Mockingbird, it is not unusual that Jem and Dill don't want Scout around. In Chapter Five, Scout notes it is common occurrence:
Next morning when I awakened I found Jem and Dill in the back yard deep in conversation. When I joined them, as usual they said go away.
In Chapter Six, however, even though Jem does his share of growling at Scout, he seems more concerned about guaranteeing her silence—whether she goes with him or not. He does not say that she can't join them, only that she has to be quiet as the boys attempt to carry out their plan: to get a look at Boo Radley under a cover of darkness.
Dill and Jem were simply going to peep in the window with the loose shutter to see if they could get a look at Boo Radley, and if I didn't want to go with them I could go straight home and keep my fat flopping mouth shut, that was all.
In this quote, the boys are willing that she goes; but if she chooses not to, she must not say anything about their scheme. Jem explains all the reasons that they are carrying out their plan the same night Dill is ready to go back home to start a new school year, rather than doing it in the summer time: no one will see them in the dark, Atticus will be otherwise occupied and hot hear "the Kingdom coming," and "if Boo Radley killed them they'd miss school instead of vacation."
Scout begins to protest, but Jem issues his last warning—not for her to leave, but to leave if she can't be still:
Scout, I'm tellin' you for the last time, shut your trap or go home—I declare to the Lord you're gettin' more like a girl every day!
Jem's comment regarding her gender (showing that he thinks she is becoming a less welcome part of the gang as time goes on) settles the issue for Scout. She doesn't see that she has any choice—perhaps Jem's comment is like a challenge, for Scout sees herself just as able to participate in the boy's activities...even if she is a girl...for her, being a girl is a mere technicality.
...Scout spends much of her time with her older brother Jem and is constantly trying to prove herself his equal.