When I say I lack empathy, what I mean is I have a deficit in understanding the emotional states of others. Hell, I have a deficit in understanding my own emotional state at times.
This doesn’t mean I’m unsympathetic.
It doesn’t mean I don’t care for others.
It doesn’t mean I can’t show concern.
It doesn’t mean I have no emotions.
It doesn’t mean I don’t get overwhelmed by other people’s emotional states.
It doesn’t mean I’m any less human than you are.
What does it mean then?
That I may need more information than a typical person to understand a social situation. That my reactions to your emotions may be unconventional. That I have to work harder to grasp what comes naturally to most people.
Simple as that. Nothing more, nothing less.