My nemesis would be a caricature of myself. She would share the same ideals as me, but she would use them as a motivation for the most horrible actions imaginable. Thus, everything I would stand for is disputed thanks to her mere existence.
She would, however, also in some way, be everything I ever wanted to be; intelligent, funny, creative, independent, diligent. A perfect human being, basically. But if that monster she is, means being perfect, then I'd question my motivations and ambitions.
Basically, her deeds and traits would prove how wrong I am about everything. How I never mange to put any sort of logic or insight into my arguments. How the things I enjoy in life mean nothing. How much of an impotent, pathetic and substandard human being I am. How no one should ever trust me or even care about anything I do.