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Jem wanted Dill to know once and for all that he wasn't scared of anything: "It's just that I can't think of a way to make him come out without him gettin' us." Besides, Jem had his little sister to think of.
When he said that, I knew he was afraid. (1.72-75)
For Jem, fear is something to be ashamed of. Maybe this is why kids are obsessed with Boo: acting like they're not scared of him is a way for them to show off to each other.