Not the OP, but I think it's because we as humans have a sort of instinctual species solidarity with each other. We value fellow humans' lives more than we value lives of other animals and like to know that other humans do the same. And not just because we're the same species with each other, but also because to the extent of our knowledge, we are the only species on the planet who are self-aware and that in itself is something beautifully improbable and immesurabely valuable and the reason why, when it boils down to it - any human is more valued by the human race than any animal.

You can love animals. You can adore animals. You can dedicate your life to helping animals and taking care of them. However, there should always be a line in the sand that you should NOT cross - that you should always value another human's life over the life of any animal, no matter how beloved.

I am personally uncomfortable about the whole 'pet is my child' thing because some people who say that type of thing blur that line, or even cross it - they equate the value of their beloved animal with the value of human life. I don't want to see a dog being called a 'brother' to a human baby. They are not equal. While the people in the OP are probably doing that lightheartedly, I don't think it's something that should be normalized and popularized.