Scout believes that the Ewells started it, and Jem believes it started when Dill got the idea to make Boo Radley come out.
Scout begins the book with a description of what happens at the end. She tells us about how Jem broke his arm when he was twelve, and explains that she and Jem disagree about the cause.
I maintain that the Ewells started it all, but Jem, who was four years my senior, said it started long before that. He said it began the summer Dill came to us, when Dill first gave us the idea of making Boo Radley come out. (Ch. 1)
When Scout says that the Ewells started it, she means that Bob and Mayella Ewell caused everything by accusing Tom Robinson of rape. This is what led to Bob trying to get revenge on the children by attacking them. He told Atticus he would get him. Atticus did not take him seriously, because he thought Bob Ewell was all talk. He was wrong.
Miss Stephanie Crawford. Miss Stephanie told Aunt Alexandra in Jem's presence … that Mr. Ewell said it made one down and about two more to go. Jem told me not to be afraid, Mr. Ewell was more hot gas than anything. (Ch. 25)
Ewell decided to get revenge on Atticus’s children one night when he was drunk, and Boo Radley was able to protect them. That was how Jem’s arm got broken.
Jem is also correct, because if Dill had not decided to get Boo to come out, he might not have gotten to know them so well and been able to rescue them. The children owe him their lives, because when they befriended him, he was able to come close enough to them.
The incident with Bob Ewell and Boo Radley is the culmination of the events that Scout and Jem's lives. They both had to grow up fast, because they learned the meaning of racism through the trial of Tom Robinson and his conviction, and the meaning of friendship through Boo Radley's overtures and his saving them.