I think there are two sides to the empathy question.
First, most modern societies are badgering pressure cookers. Push push push, pressure. Thou shalt think this, thou shalt feel that. They'll take any stick they can beat you with. Empathy is just another one they can use. You must feel such and such way. Essentially, if somebody stubs their toe, you are supposed to feel the pain. If someone's house burns down, you have to feel as if it was your house. That's just so wrong. That's not empathy. How does that help, if you tell me a sad story and I start to sob and moan and cry in your stead? Let alone if we are discussing a third person we don't even know.
If anything, empathy is holding still and not heaping more shit onto a person's struggles (including your own). Empathy is not telling anyone how they ought to feel, but asking them how they actually feel. Including yourself. Empathy is not pushing a solution, or giving a gift they didn't ask for. Empathy is asking "What do you need right now?" and trying your hardest to hear the answer.
Some people are better at assessing what a person needs (including themselves), and the fewer questions you need to ask to do the right thing for the person, the better you are at taking their perspective, i.e. the more empathy you have. You need both hemispheres to assess all sides of a situation. You can look at something this or that way, if it were me I would want this, but knowing how they are I think they would need that, and then all other kinds of learning, implicit and explicit, that influence your behavior in how you relate to others.
If your brain hemispheres don't cooperate well, either because you're dominant in the left one (autism) or the because remote control switches erratically between the two (adhd) or because you're dominant in the right one (dyspraxia), then yes, seeing all sides of a situation could be affected. (Nevermind front-to-back and top-to-bottom brain imbalances, etc etc... )