Jem is proud of atticus because

atticus is a great shot

atticus is decent and humble

atticus saved the neighborhood

atticus is old

atticus saved the neighborhood

Atticus is a great shot

Explanation:

As the story advances, Jem and Scout start to see their father from an alternate perspective. When he shoots the out of control puppy, Jem and Scout are awed. They had no idea that their father was a sharpshooter.

This is an instance that alters their perspective on their father being old and weak. Rather, they consider Atticus to be a hero. They appreciate his shooting abilities.