Sleepy fish and others who have asked for logical/objective reasons for saving the human, here are the ones I could think of:
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- Mill/Bentham's fundamental axiom: the 'right' thing to do is the one that ensures the greatest happiness for the greatest number of people.
Family pet dying will only affect you and your immediate family. Person dying will affect their parents, children, aunts, uncles, grandchildren/parents, friends, co-workers, employers/ees, and more. These people's sadness may very likely have an adverse affect on their immediate and wider circle of acquaintances, and so on.
*2) Utilitarianism again: an average human will live longer than the average dog. Therefore the decision will have a positive outcome for longer. (although I don't want to open a new can of worms, surely most people agree that in a similar scenario they would save an unknown baby/child over an unknown adult)
*3) Possible future potential. A dog will never become prime minister/set up a charity/donate blood or organs/invent something that increase the quality of life for humans and/or animals/write a novel or create a work of art that influences millions/even become a doctor or firefighter that saves others in a similar hypothetical situation.
*4) Reason. Animals can of course feel pain, but they cannot rationalise/understand it in the same way humans can. If left in the fire, they would not feel the full spectrum of emotions (betrayal, terror, panic, loss, despair) that a child or adult would.
Would be interested in hearing any rebuttals/additions