WHY ANIMALS DO THE THING

Some of both, really. 

There’s a lot of anecdotal evidence that domestic dogs and cats understand that baby humans are not full-grown humans, and they’ll often be extremely tolerant of or even very attached to human spawn. They’re often very gentle and tolerant with babies of their own species, so it’s not really surprising that - assuming they understand baby = small human - they react to human babies in similar ways. Similarly, dogs that have never encountered babies or toddlers tend to be a whole lot less comfortable around them, and don’t modify their behavior and communication as much when interacting with them. 

It’s also totally possible to teach dogs and cats (but mostly dogs) to accept a new baby in the house - but this generally results in the dog not stressing / being afraid of the baby, rather than suddenly liking it. 

I will also add that part of what you may be seeing in some of the videos - and I can’t tell you for sure because I don’t know what you were watching - is learned helplessness. Western culture has a really bad habit of assuming that our pets should like our babies and pretty much forcing them to put up with really rude / uncomfortable / painful / inappropriate treatment from little kids. A lot of times what looks like a cute video of a dog and a baby is actually a really uncomfortable dog signalling desperately that it would like this to be done now, please. That’s why so many times when a dog bites a kid people say it “came out of nowhere” - not because it did, but because they’d been ignoring the dog’s signals for so long that the dog finally ran out of ability to tolerate things and communicated it’s discomfort in the only way it knew how.