What does Jem say to get Scout to go along with the plan to peek into the Radley house? Why does she disapprove?
The plan to peek into the back of the Radley house appears in chapter six. Technically, Jem and Dill don't invite Scout initially because they know she would be scared and object. But they couldn't shake her on the last night of summer vacation, so after she presses them a little bit, they divulge their plan to her. Scout doesn't want them going to the house for the same reason that she wanted them to stop playing out the Radley's family drama in front of their house--she knows that Arthur (Boo) Radley watches them.
Scout knows that Boo watches the kids because after Scout was rolled in the tire right up to the Radley's porch in chapter four, she heard someone laughing from inside the house. This was proof enough to her that Boo exists; and based on the stories that he prowls around at night, Scout worries that he might look into her window one night for revenge. As a result, Scout tries to convince Jem not to go peek through a window to see Boo Radley that night. Jem says the following:
"Scout, I'm telling' 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!" (51-52).
Scout says that when Jem said that, she had "no option but to join them." This is the second time that Jem has complained about Scout acting like a girl; and for a tomboy, that's about the worst insult she could hear. To defend her honor, Scout had to accompany the boys along on their mission to view Boo Radley from the broken shutter at the back of his house.