When we say something is "cute," we typically mean it's somehow attractive or appealing in a way that makes us want to protect or otherwise take care of it.
Colloquial versions of this term also refer to things that are attractive in other senses, or things that are not serious or professional. But the typical, psychology- and biology-related definition orients around the triggering of a nurturing response most people experience as at least somewhat pleasurable.
Cuteness can also trigger aggressive behaviors often called "cute aggression," which manifests as a desire to pinch or squeeze or bite or even harm something that seems "too cute."
Early modern research (which followed far less legitimate research by a Nazi in the 20th century) into this seemingly discordant response to cuteness suggests it might be related to the brain topography activated by our perception of cuteness: the same neural structures are lit up by both aggressiveness and cuteness.
There's also a chance that our neurological reward systems (which seem optimized to nudge us toward caring for cute things, like our offspring) are to blame, releasing dopamine when we engage with things we consider to be cute, and that reward-release increasing when we engage more effusively (even to the point of squeezing a puppy or baby until they have trouble breathing).
Formal research into cute aggression is newer than research into cuteness more broadly, so we're still working with a lot of maybes and few well-performed studies.
We do seem to know, though, that some animals—especially those that have co-evolved with humans—have developed physical traits we associate with human babies, and those evolutions have paralleled our more-humane treatment of them; and "baby fat" chubbiness, large heads, and big eyes are some of the traits most cultures associate with infants, and thus, cuteness.
So while cuteness can elicit physical violence (often of a relatively moderate variety, like squeezing and pinching), it would also seem to be a means of tempering the violence associated with viewing some animal species as sources of food or as pests that need to be killed (rather than as cuddle-able members of the family).
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