(H1) Knowledge and Talent

I talked with a girl the other day who is a music major, specializing in piano. She has been playing piano her entire life and can sit down at any piano and churn out Chopin no problem. She is very talented but if you talk to her about it she will say that she can still improve and she's only kind of good.
The Dunning-Kruger effect came about by a study conducted by Cornell university psychologists David Dunning and Justin Kruger. The results of this study stated that people who are not very good at something will overestimate their skill at the given activity. For example, if someone isn't necessarily the smartest, they will overestimate how intelligent they are. There is a reverse of this effect as well, people who are highly skilled at something or highly intelligent will underestimate their skill and knowledge, constantly believing that they need to improve, an example of this being the girl who I mentioned above.
This type of cognitive dissonance can make it hard to talk to or reason with people, most especially if they are of the side lacking in talent or intelligence but believing themselves to be in abundance of it. How can you talk to someone like this rationally and achieve thought-provoking discussion when they believe they have no room to grow? In Plato at the Googleplex, Plato struggles with this situation when he talks to an abrasive television personality.
I think we should all try and be aware of our own abilities and limitations, so that we don't accidentally reject or shut out the opportunity for growth.