I think the term "care" has several layers.

For instance, do I care about strangers that I don't know? Personally, my care towards them is more on an intellectual level, in that I wouldn't want to wish harm on people and if someone was injured, I would either try to help or I would want them to recover ASAP. I care because I respect the sanctity of life and I think everyone deserves the best life possible - which includes a life without pain.

However, do I care from an emotional point of view? Honestly, I don't...and there are actually very few people in my life that I can honestly say that I care about emotionally. Then again, I do have some issues with empathy so I'm probably not representative of most people.