People make a big deal about not caring what anyone thinks, and then they become spiteful dolts over the silliest things. It's as if what they really want is to warn others not to care what they think, so they can opine recklessly in reaction to others. The old two-way street clogs up. Many seem, by this prosaic "not caring" heroism, to be admitting their own opinions tend toward moronic jerks of the knee.
I care what people think, and that's in part because my thoughts are worth something; I want people to care what I think in turn, given that I care what they think.
It isn't that *I* think it, or that I *think* it, but that I have put a lot of care into the thought. That is why I think others should care, and it is why I care.