I used to think that I didn't empathize, but that is absolutely false. I kind of have to or I'd be really crappy at the career I'm about to go into. I think it's more that I dislike whining, which I hear a LOT in my line of work. I can't tell you the number of times I have been at work likely feeling worse (I get migraines sometimes...can't call in sick for all of them) than the person who was crying, screaming, moaning, yelling at me, refusing to walk to the exam room, etc. In that case, my empathy tank is running on fumes.
The feedback I've had from others is that I am, indeed, quite empathetic. I tend to believe that, now, and in fact I remember being a child and wanting to take care of everything. I mean,
everything. I once saw a beautiful orange leaf in the street that was being tossed around by cars and I took it home with me and put it on my windowsill, in the sunlight.

I was a weird kid...only child.

I think that I can build walls around certain feelings/emotions that I feel may overwhelm me, and empathy may be one of those emotions.