I suspect that there is an element of speciesism underlying this juxtaposition. Speciesism is a kind of prejudice involving the belief that humans are more valuable than other animals simply because they are human. Like other forms of prejudice, speciesism often goes unrecognized and unacknowledged by individuals, and is best identified through looking at the language we use.
We love dogs, and we want to do right by them. When we try to express just how much we love and value dogs, however, we find ourselves resorting to human terminology, like "baby" - never "just a dog". This pattern of language suggests that, in our value system, something has more value when it is more like a human. If we want to express our high regard for something, we tend to use language that points out the human-like traits it has, like "my dog's so smart", or "dogs are amazing because their brains process emotions like ours do".
But what is wrong with dogs just being dogs? Why do we have to humanize them to justify the love and and care we give them?