Remember that in VN, Kirei clearly stated due to his inability to truly feel affection, he never loved his wife and even his children. He confessed that despite his effort to try to love them, his heart is simply couldn't understand it.
a_bill said: Maybe he did love but just went batshit insane after, thinking that he never loved it. But that's just a theory.
He was born without the capability of loving another individual because of how evil he was. No matter what he did, no matter how hard he tried, he couldn't be 'good'. Which explains why he's a priest, he went as far as he could to 'do the right things' in life, but he never felt anything out of it. He also married and had a child, but due to his forced evil nature, he couldn't truly love them. It was all in an attempt to be a good person, which he was born evil. It's not his fault, he honestly tried his damn hardest not to be evil, but he just couldn't feel the good. Through his whole life with them, he never loved them, it was just a job for him.
And he was never batshit insane, he's simply relaxed evil, and has been his WHOLE LIFE.
Its more that being a sociopath means that you are more likely to commit evil acts. The difference is that apathy is a complete lack of interest in the sense that you really don't care, sociopathy is that you are unable to show empathy for other people or "love" in the traditional sense.
The current medical definition requires some degree of either passive-aggressiveness or malice, but the idea is more that this is a person that could be eating breakfast with you, slit your throat, and go back to breakfast without flinching. Its the classic example of it.