I do care about people. Over the years I've learned what are the kind of things that make people tick. I can often dissect what they're saying to get to the root of what's bothering them. Sometimes even revealing something to them about what may be going on inside of themselves. I suppose it's an analytical NT thing.
I can be around suffering sadness and anger without it changing my mood or being scared off by it. I don't know how empathetic I truly am though. I don't try to draw anything out of anybody. I sometimes want to know what people see in me. A lot of people will reveal deep personal stuff to me, like literally confessions of breaking all of the ten commandments, and I never do anything for them. Until right now I never even wondered was I supposed to. I don't know why they do this. I've never asked. Not even sure of the repeat customers. Though I've gotten a few "I've never told this to anyone before…"'s.
If there's a natural inclination I think it's to alleviating discouragement. I'll generally let people rant or boo hoo but when they talk about giving up, it's hard for me to not say something to point out that things aren't as shitty as they may appear. My only pithy saying is the Chinese proverb of "the man who walks a mile a day will eventually make it around the world." I'm not really a hang in there, things will get better kind of guy but I will point out alternate methods or make suggestions or try to convince people it's not over yet.