Well, I am also offended by your stipulations. Now we are both offended. Let's use this as a chance to practice seeing eye-to-eye even in the face of irreconcilable moral differences, eh? It's a skill we're probably going to need as a civilization.

Now, the specifics - it seems to me the particular moral axiom in question here is that "human life is always worth more than non-human life". Others in this thread have pointed out that you can't use that to make statements about what sort of grief people ought to feel, and I would hope that whatever your moral framework, compassion for grieving humans (whatever their moral framework) should factor into it.

However, I also think it's worth tackling this particular moral axiom head-on. The value of a human life is not constant or consistent between people - your own family is worth more to you than a stanger's, and you even admit that a dog might warrant more grief than a terrible person, even if that terrible person is family. Well, the value of a canine life isn't constant either. If it's possible and justifiable to love a dog more than family because the family is bad, why shouldn't it be possible and justifiable to love a dog as much as family, because the dog is good? There's a continuum, not a hard cutoff of "humans > dogs". Even if you think the average human is worth more than the average dog, you shouldn't be surprised - or offended - by other people's bereavement.

(I'd like to add an argument-from-Hollywood: They even made a whole film about a man cutting a swathe through evil, violent mobsters in a righteous fury, because they killed his dog. They made a very similar film about a man doing this because evil, violent mobsters kidnapped his daughter. Clearly, the emotions are comparable, and according to hollywood dogs and family are both worth more than evil, violent, human mobsters).