In Lee's To Kill a Mockingbird, why doesn't Jem want anything to do with Scout at school?

Jem is older than Scout, and he has had several years of school experience by the time she starts the first grade.  Jem takes Scout to school on the first day, but gives her strict instructions.  As they walk, "Jem [is] careful to explain that during school hours [she] was not to bother him... [and not to] to embarrass him with references to his private life" (To Kill a Mockingbird, Chapter 2).

At...

Jem is older than Scout, and he has had several years of school experience by the time she starts the first grade.  Jem takes Scout to school on the first day, but gives her strict instructions.  As they walk, "Jem [is] careful to explain that during school hours [she] was not to bother him... [and not to] to embarrass him with references to his private life" (To Kill a Mockingbird, Chapter 2).

At school, Jem wants to maintain his reputation.  He does not want Scout to say or do anything which will embarrass him.  At home, they often play together.  They play imaginative games, such as when they act like the Radley family.  At school, Jem tells Scout not to expect him to play Tarzan.  At recess, he does not want Scout to follow him around.  He tells her to spend time with other first graders and let him do his own things with his own friends.