Good question! I think it's because cats often bring home dead birds, or dead mice, to their owners. So the idea is that you look like you've been eaten up and spat out!

Yeah, it's like Ryan said. Cats kill birds and mice and bring them to their owners, obviously looking disfigured, disheveled etc, from the struggle. Another version of this is phrase is the exclamation: "Look what the cat dragged in!" which is used to acknowledge someone's appearance/arrival. E.g. "Look what the cat dragged in. We were just talking about you." And another common phrase that uses the word 'drag' that has the same meaning is: "to look like you've been dragged through a hedge backwards" E.g. "I bumped into Mary up the town the other day, she looked like she had been dragged through a hedge backwards." (she looked extremely untidy, scruffy etc.)