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Jem loves Scout, but he is definitely going through the stage where a sibling isn't exactly who you want tagging along all the time. Jem is maturing; Scout is just a little girl. Jem doesn't want Scout around at times simply because she is 'a girl.'
Jemis far more quiet and reserved than his sister is, therefore there are a few moments where he's exasperated by her behavior, but on the whole they enjoy each other's company, feel a great deal of loyalty toward each other and a great deal of love.
Jem is Scout's big brother. In the beginning of the book they are playmates, spending the long hot Maycomb summers together in seemingly endless play. As Dill shows up and Jem matures the dynamic changes. Jem does not engage in play as much but becomes more authoritative and protective of his little sister. Jem looks after Scout and it is evident throughout the book that he loves her.