Popular Science has a story about "Why do we want to squeeze cute things?" that demonstrates something like a predatory connection to cuteness:
But for the sake of thoroughness, researchers did a second experiment to test whether the aggression was simply verbal, or whether people really did want to act out in response to wide-eyed kittens and cherubic babies. Volunteers were given bubble wrap and told they could pop as much of it as they wanted.(H/t: InstaPundit.)
When faced with a slideshow of cute animals, people popped 120 bubbles, whereas people watching the funny and neutral slideshows popped 80 and 100 bubbles respectively.
Now they posit a couple of theories about this that point in other directions. Still, I think I'm right: there is something about the kind of mind you need as a mammalian predator, as a predator who hunts by thought rather than by pure instinct, that gives rise to this.
Consider further anecdotal evidence:
Now why is that, I wonder? But I think it is.