“I Won t Back Down” is the first single from Tom Petty s first solo album, Full Moon Fever released in . The song was written by Petty and Jeff Lynne, his . I Won t Back Down Tom Petty remembered. By Frank Pallotta, CNN. Updated PM ET, Tue .Day ago “That song frightened me when I wrote it,” said Petty. “I Won t Back Down” was written in the studio while “Free Fallin ” was being mixed. George Harrison, who performed background harmonies, told Petty that a line about “standing on the edge of the world” was dumb so he .