Having a pet is a reliable signal that you'd take care of children, maybe?

People with a preference for pet owners end up with children with a caring parent, creating selection for attraction to pet owners.

Then, once there's attraction to pet owners, there's sexual selection for pet ownership.

So, if finding animals cute makes you more likely to be a pet owner, it gets selected for.

Predictions:

• We find specifically the animals that make good pets to be cute. Animals that are violent or hard to access we find less cute.
• Pet owners that take good care of their pets are more attractive than non pet owners, and bad pet owners.
• Whichever sex is made more attractive by being a loving pet owner (I'd guess males) is also the sex that finds animals to be cuter.