Do you care what people think? Is it even possible not to?

If we trust that we’re part of the animal kingdom, then we live in packs, and beyond any physical attributes that have been replaced by awareness and intelligence, we thrive on psychological and emotional levels right?
Generally, living among and communicating with others is what makes a healthy human. While you can become a hermit and live in solitude, apparently that can lead to insanity which isn’t a good sign of what we’re supposed to do, or be. I think…(Corrections appreciated.)
That’s not really the point, but merely some slight ball rolling to explain the following;
I often see people who say they don’t care what others think or say about them. But I notice said statement is often presented with much vehemence and emotion, usually as a response, quite a natural one I think, to something that has been said of the person in negative light. Which basically proves the entire contrary, that they DO care. Otherwise if they really didn’t, why would they bother to make it so clear? Why would they be so upset? It’s natural to want to be recognized isn’t it? A vital part of making it in society maybe?
Apathy is apathy, not a defense mechanism. Or is it?
On that same coin, if you say something nice and supporting about a person, they’ll be happy and satisfied, which is also natural…but they’ll never say they don’t care what you think.
I mean if you really didn’t care, that would include both positive and negative feedback.
Or maybe I got it all wrong. I think what people are trying to say is that they won’t let people’s views thwart them from their path, whether they care or not. Or am I not thick skinned enough? I always act like I don’t care, but I still do, yet I can’t ever really find any reason why I should. (Hence the whole idea of it being natural but maybe that’s just me.) What do you think?

Feel free to take the subject beyond individual perception though. Apathy probably covers a lot of things. If apathy as we define it exists.