Empathy or liking of someone or something.

Paradox: where people do care yet it appears nobody cares

Rather, it's probably not a paradox at all; it depends on exposure, their personality, etc. There are both - strangers liekly not care, but parents likely have some level of care - but too much care (about the wrong things) might actually put pressure, just like if parents care too much about school grades and not that much about their child's well-being - of course something would go wrong.