The story
From dog + eared (“having ears (of a specified type)”), modelled after dog’s-ear (obsolete), due to the similarity of their appearance to the folded ears of certain dogs. The word is analysable as dog-ear (“to fold the corner of a book’s page”) + -ed (suffix forming possessional adjectives) (dog-ear is attested in print later than dog-eared).
Etymology from Wiktionary, CC BY-SA 4.0.