Not noticing/caring about other people's feelings might be some kind of autism-spectrum disorder comorbidity (from what I understand, ADD/ADHD and autism spectrum disorder occur together pretty frequently[0])
Not a psychiatrist, just wanted to mention it as something you might consider, that you or other people reading this might not be aware of.
In my experience, it's not that you don't understand or can't comprehend how other people are feeling: it's that you just miss it a lot of times, because you're not paying attention.
We can understand how people feel, but it's usually not something that pops into our heads, because we're distracted/occupied with something else.
In cases when we're not (rare, and as assholish as it is), we can care about and work with other people's emotions.
Agreed, what we have is often simply dismissed as selfishness or self-centeredness. It’s hard to keep tabs on others’ emotional state when there is so much going on upstairs all the damn time.
I think people tend to get too attached to the medical taxonomy which has some clear problems.
In my case I think the rationalization of emotions and the dismissal of irrational emotions is a coping mechanism that was brought about by hypersensitivity. Later on I had brain inflammation (CFS/ME) which inhibits emotional response as well a a host of other hormones. I now have effective medication, but I’d still rather not deal with other people’s feelings.
Not a psychiatrist, just wanted to mention it as something you might consider, that you or other people reading this might not be aware of.
[0] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4010758/