You can be fired for just about any reason in the United States.
Now, if you're asking whether or not "lack of empathetic communication" is a real thing worth firing somebody over, that depends. Certainly interpersonal abuse is something that can happen and can rise to the level where it becomes a good reason to fire somebody.
In this case, we largely do not see most of the communication that took place. We really only have her word to take that it wasn't that bad or not worth being fired over. We also don't see much in this story about how her behavior affected the people around her. So, I wouldn't draw a conclusion on whether or not the firing over "empathetic communication" is appropriate.
Now, if you're asking whether or not "lack of empathetic communication" is a real thing worth firing somebody over, that depends. Certainly interpersonal abuse is something that can happen and can rise to the level where it becomes a good reason to fire somebody.
In this case, we largely do not see most of the communication that took place. We really only have her word to take that it wasn't that bad or not worth being fired over. We also don't see much in this story about how her behavior affected the people around her. So, I wouldn't draw a conclusion on whether or not the firing over "empathetic communication" is appropriate.