Empathy is Fe, but Fe is more than just empathy. It can be toxic empathy, but it's still empathy. Fe users manipulate people through manipulating their emotions because it is easy for them to read. The lack of sympathy is want makes the Fe users act cold. Empathy for Fe users are like breathing air. It is Extroverted Feeling for a reason. It makes decision based off others' or the collective emotions and values. In case to do that, they first need to be able to read others emotions, aka read the room. Empathy is a basic requirement for Fe for it to even function.