>Say that you chose a stranger over your dog. Then that stranger went and killed another person. Would you regret your decision?
No. Because I still would have made the best decision possible at the time given all available information. This is the same argument essentially as the death penalty question. Someone else's violent act can never vindicate your own. That's only valid in the case of immediate self defense. Although if you take this argument to it's logical conclusion, which would be "Kill a thousand dogs, or hang Hitler", I'd have to admit it becomes pretty indefensible. So the real moral choice probably lies somewhere in-between.
>How do you choose to save a stranger's life without knowing anything about them and what they're like?
It's faith in the fact that any single given human life has more intrinsic value than any number of any animals. I'm essentially putting myself in that situation. Would I be ok with dying to save a dog? No, never. And so I extend that to every other person. Obviously this only works with animals. Would I feel the same about a person I love instead? Absolutely not.