The fact is that everyone – on some level – cares what other people think. So the more you try to act cool by making a show of how much you don’t care, the more you betray the image you’re trying to project. Caring about things or what people think is not the issue. Letting other people have control over your sense of self-worth is.
If you’re trying to earn affection or gain favor by propagating whatever sentiments society considers cool at the moment, you’re likely far more guilty of approval-seeking than you want anyone – including yourself – to believe.