Writing believable characters with which an audience can have a cognitive and emotional connection is the key to an excellent story. A believable character, one that allows us to suspend our disbelief and immerse ourselves in the narrative, is a character at odds with a fundamental drive of the author as a human being.
We don't, in our daily interactions, reveal the whole of ourselves. It is in our best interests and in our very nature to present those aspects of ourselves that are most advantageous, most desirable and least likely to spark conflict. We strive to perfect ourselves, at least publicly, minimising and obscuring our flaws as best we are able.
Part of the problem is that we are all too aware of our own flaws and cognisant that others share similar failings, we know that nobody is perfect even in a world where everyone is trying hard to look like just that. We're also pretty good at finding each other's shortcomings, and picking out the patterns of behaviour that they cause; observing how our flaws influence our choices and our actions.
It is because of this that the perfect character in a fictional work jars and disinterests us. We find it hard to invest in a persona that embodies what we strive for but can never achieve: flawlessness. We know that despite our efforts to the contrary we cannot master every discipline, make all the correct decisions and understand every problem. We reject any portrayal that gets too close to this ideal person.
There are narrative problems with the perfect character. They become predictable, they always have the answer, the talent or the knack. They always get the girl, are far too smooth and far too important. They become rapidly predictable and sickening in their perfect influence. The ideal outcome is always guaranteed for these über-humans. Tension and suspense fall by the wayside as our expectation is of imminent success.
A good character mirrors the imperfection we hold in, that we like to believe is a secret and still take comfort in our knowledge that it is ubiquitous.