In A Day No Pigs Would Die, doing your duty is a priority. (And yes, we chuckled a little when we wrote "doing your duty.") In the Shaker way, it seems, every individual has a "mission," something that they're meant to accomplish. And getting the mission done is a measure of how well they're fulfilling God's purpose for their life. Sacrifice, hard work, and facing up to your responsibilities are all marks of a duty fulfilled. Sounds a lot like Papa's principles, huh? Yep—duty is kind of like principles in action.
Papa's sense of duty is so important to him because it's what keeps him going day after day. If it weren't for his sense of duty, he couldn't go on.
Rob's duty to be a good pet owner is stronger than his duty to follow a code of behavior imposed on him by Papa. He should have found a way to keep Pinky alive.