I have children and a dog. I wouldn't say my feelings towards my dog were on par with my feelings towards my children, but they're of a similar nature - things I love and look after. A part of my family. Yes I do place a higher value on my children than my dog, but I do love my dog. The idea of something happening to him makes me very upset. I try my best to make sure he has a happy and complete life, it is relatively short after all.
My children feel the dog is a family member, the dog brings them huge joy. When my son was having some emotional problems he would curl up with the dog. Animals can have a huge role in people's lives.
I think the issue basically is that people are unnecessarily nasty about loving a dog. There's nothing wrong with seeing your dog as a family member, it's not hurting anyone else to feel that way. It's not for one person to tell another their feelings are wrong or to belittle something something feel they love.
I will leave my dog at home for the half the day on Christmas day because my in-laws have very poor health and he's too rambunctious. My children are also rambunctious, but I wouldn't leave them at home.
I'd also never leave my dog in kennels because of the type of dog he is - he'd be utterly bereft and absolutely would not be OK. He gets upset when one of us stays away from the house one night. I'm lucky in that he can stay with my mum if we go on holiday, he's upset but OK. So it's about having a reasonable balance. My children are also upset when I go away for work, but I have to do it anyway.
So it's not quite the same with chilren and dogs, but I also can't see why we can't just respect the feelings of other people. If they feel their feelings for their dog are on-par with the feelings for their children - who are you to tell them otherwise?