To not experience emotional pain is what would be interesting.
CS Lewis addresses this obliquely in The Problem Of Pain. In a nutshell, Lewis addresses the standard agnostic/atheist argument about how an omnipresent and all loving God could allow for pain. Lewis concludes that pain is a necessary condition for growth, and it's precisely because God does love us, that we are put in situations that cause us pain.
I'm fairly confident the mother in this story loves her daughter dearly, and yet wishes she were able to fell pain...
Are you referring to sociopathy, the total lack of empathy? I can think of a couple of politicians who show symptoms of that - though I suppose that even taking narcissistic offense (narzistische Kränkung) must be regarded as a form of pain.
Regards,