If you read the first part of Chapter 10, the incident where Atticus pops Old Tim Johnson the rabid dog, you can get a pretty good idea of why Scout and Jem are ashamed of their father.
He is old, he started late on having kids, he won't play tackle football, he works in an office, he doesn't drive a dump truck, he isn't the sheriff and did not work as a mechanic or anything at all that "could possibly arouse the admiration of anyone." People talked about him, sure, but they didn't do so because he was tough but because he was involved in the Tom Robinson case.
In the beginning of the novel, Scout and Jem do not think Atticus is very manly. They also do not think he can do anything useful. He is a lawyer and the studious type, so when Miss Maudie tells them that he can write an "airtight contract" and is a top-notch lawyer, they are not very impressed. Nor are they impressed when she tells them he is an excellent checker player.
However one day, they see a mad dog foaming at the mouth coming down the street. Heck Tate is there and he tells Atticus to take a shot. Scout and Jem are shocked, because they have never seen their father shoot and have always thought he was opposed to guns. He has given them air rifles, but did not teach them to shoot. Their uncle had to teach them to shoot. Heck informs them that Atticus is one of the best shots in Maycomb. Reluctantly, Atticus gets his gun, fires and fells the dog with one shot. This changes the children's view of their father immediately.