Emotional Detachhment

How would you define "emotional detachment"? What are some examples of this?
I don't really understand this.

A close family-member of mine once died in a very nasty way indeed. I was on good speaking term with that person. Nevertheless there was nothing more, then an unemotional thought of how sad it must have been for said person(s). Others broke down, whilst I didn't understand their emotional states.

Or… once I thought to have a progressive incurable and possibly deadly disease. Whilst waiting for the final diagnosis, I just thought about how to rearrenge my further living, if necessary and went on with life. I didn't break down, spoke to nobody, aside the doctors, about it.

The emotions are there! I felt sorry for said family member. But aside from recognizing the presence of that… pale emotion, was nothing. Not more indeed, than I assume, that you feel about reading my words right now. As I awaited the diagnosis from the specialists, my thoughts circled endlessly around said topic.

But it was more of a logical analysis about what have to happen next and some kind of bucket-list. I neither cried, broke down, nor did I blame the world for what I may face. I went on as usual. I guess, that the "normal" reactions were somewhere deep insight me. But it felt, as if they had no connection to me, barely recognizable as they were.