The ability to reflect upon oneself is called:

Reflexibility

Sociology can show you what you look like to others; it can teach you how to look at yourself ‘from the outside’, so to speak. This is called ‘self-reflexivity’, or sometimes just reflexivity. This is the ability to reflect upon yourself, to turn back your gaze (which is usually directed outward) back towards yourself. But this self-inspection must be critical – i.e., it should be quick to criticise and slow to praise oneself.