The feelings we have about ‘self’ are based on usefulness. In other words, if you didn’t CARE what others thought of you – you wouldn’t function very well in society because you would be an outcast. So a strong sense of self is a necessary part of being an individual. It’s a useful tool for society.
If you were alone in the world- you wouldn’t need a self. (And in fact you wouldn’t have anyone else to compare yourself to, so you couldn’t define your self) But because you’re around other people and you require their help and interaction – a self, especially a self that others perceive as valuable (whether in the form of attractive, knowledgeable, resourceful, etc.) – is very useful in society – that’s why you care how others see you.
You can use this knowledge to develop a really powerful self, one that is attractive, confident, etc. But just remember not to care too much what people thinkÂ about your self (not to the point of suffering). The easiest way to do this is through balancing engagement and withdrawal. When out in public, engage others, enjoy being inside your self. When alone withdraw and remind your self how temporary life is, remind yourself of death constantly so you don’t get attached to self (which causes suffering).