Someone who is the complete opposite of me would be outgoing, altruistic to the point of complete disregard for her own financial well-being, a militant gods-hating atheist without a spiritual bone in her body, completely asexual and not in the least affectionate or physical in a relationship. We wouldn't get past the first date.
On the other hand, if I were to date a girl who was exactly like me only with the opposite parts and a missing Y chromosome, that wouldn't end well either. We'd both be so passionate, so intense in our emotions for each other, and yet so conflicted over finding a balance between love and life's responsibilities (and our own personal projects) that it would inevitably degenerate into either codependency or resentment because neither one of us would be able to keep the other one grounded in reality. It would be one hell of a great five or six months, but it'd crash and burn. Or I'd get her pregnant...and heaven help the world if that were the case!
My virtues would cause me to see an opposite as horribly flawed. My flaws would cause me to see a "perfect match" the same way.