Why do we think that recognizing oneself in the mirror is strong evidence of self-awareness?
Because it correlates with intelligence and seems indicative of deeper trends in animal neurology. Probably not a signpost that carries over to arbitrary robots, though.
Apparently a PhD candidate at the Social Robotics Lab at Yale created a self-aware robot:
What do Less Wrongians think? Is this "cheating" traditional concepts of self-awareness, or is self-awareness "self-awareness" regardless of the path taken to get there?