> Some people really do feel emotions of others before being able to rationalize it.

Yeah, they are called empaths. That's empathy. Rationalizing is another process, which can be done faster with high emotional/social intelligence.

> psychopath - i.e. someone who can rationalize and think about other beings logically, without actually being able to subconsciously empathize.

Exactly. Low on empathy but high on intelligence - psychopath. Low on emotional intelligence but high on empathy - empath. Low on both - unfeeling idiot. High on both - a warm kind person.