I saw this story in an anthology in a used bookstore in 2009.
When the aliens came, we negotiated a peace treaty with them. Everything was going fine until they said "oh, and you'll have to stop keeping dogs as slaves, of course."
Humans said "what? No, they're not slaves, they're pets. They're not sapient!"
Aliens said "THEN IT IS WAR."
This is backstory, told as man and little girl and small dog run through the remains of a city while trying to escape an Alien Death Machine. The machine traps them under flaming wreckage, then tenderly extracts the dog, apparently to bring it to a re-education facility.
As the man's life ebbs, he thinks "at least they didn't find out about the pigs."