He claims he got it in a hard-won battle with a rival terrible Sharptooth, but the truth that he's too embarrassed to reveal is that, back when he was a reckless teen, he had tried chasing some prey through a narrow rock passage and ended up scraping the side of his face and body along a particularly sharp point along the rock wall (and to add insult to injury, that prey has also gotten away).
What happened to Ducky's father?