Empathy

From wiktionary:

empathy (uncountable)

1. the intellectual identification of the thoughts, feelings, or state of another person
2. capacity to understand another person's point of view or the result of such understanding

Empathy is not just being able to think as if you were in somebody position. Let's call this first-order empathy.

Empathy is thinking as if you were that somebody else, in that somebody else's position. Let's call this second order empathy.

A selfish person, employing first order empathy, would take his selfish viewpoint to that other person's situation - and would imagine what that other person would do, if he were selfish like me.

Second order empath is to imagine what that other person feels. If you are selfish bit they are not, imagine what an unselfish person would feel. And vice versa.

Empathy is not necessarily sympathy. I may be able to imagine what Hitler felt, but I do not feel symapthy for his views.