There is no "how it feels to lose a X", there is "how throwaway713 felt when they lost X". One may have a good but not very deep relationship with a close family member, but spend every day with their pet for 15 years, so to them it might be comparable.
Of course, saying "I know how you feel about your mother cos I lost my dog" is incredibly insensitive and stupid.
> you're going to claim that it is comparable to lose a human being that meant everything to you because an animal died
If that person was that important to you, of course it's not comparable. I don't think that's what the other comments were saying though.
I lost grandparents I was close with; one was after many years of several diseases fighting for the kill, death itself came as a mercy. I love my dog dearly, he's very old and his last breath is near and I get teary-eyed just from writing about it. And still, he's nothing compared to the loss of my grandmother. But that's me.