What is a good way to describe what it means being highly gifted to a person that might have skepticism or criticism towards the subject?

One of the problems I generally have to work on as an issue in therapy is smartness. So many people picked up a shame belief from it because of primarily having education being a marker or having emotional issues override their good sense. On the other side I have people who were promoted as being very smart. (Gifted is the PC word now) and no one can stand them. They think right answers are the end-all be-all and of course, THEY being the smartest, naturally assume THEY must have the answer everyone is looking for. I am going to assume the gift you are referencing is not a talent like art or music but the individual you are concerned with feels not good enough, unqualified, and believes somehow they were able to fool and manipulate the system to get where they are. Impostors disease. The skepticism is generally from some injunction done to them from one or more authority figures. The less identified kid was shamed or humiliated at some point. Sometimes it just is having a wiz kid sibling in the family for whom the preferred dynamics come easily. Those kids are typically terrible markers for everyone else. To help, most of the time it is looking at other parts of their life and clearly seeing the decisions and choices made, had to be done with an intelligent weighing up of the data. I also go through how the educational system really works and that it generally isn't a good marker for intelligence. Grades typically reference time attending to the subject, not ability. Sometimes when all else has failed, I will give an IQ test. I already have a pretty good idea what theirs is, so would not give one if I would be worried they could mess up. Even then, they still tend to cancel the facts out. They have experienced the truth after all. There's a filter going on which is why you are having trouble getting through. I call them, guard dogs to the psyche. The truth is internalized from the child's experience and you are going to have a terrible time using logic to counter it. That's why a major prescribed method is to be put in a situation in which the person goes through a new intense experience, overriding the original one. The problem with this of course is, many times, a lot of training has to be accomplished and everything has to go smoothly. Because it is a belief, a fear, and realization is the cure; I try to use processes which opens it up. Changing perspective generally gets the job done. I have posted a number of different ways on other answers. Using chairs, camera 1,2,3 and getting the blessing are but three. Your focus is to help them access where the injunction came from. Then they can listen to a new perspective, and then they can acquire the skills to utilize the new found ability. Good Luck.

I agree you shouldn't use the word gifted for what you are talking about - that is usually related to IQ. However, I know what you are talking about.  Here is what I did one time while explaining it to a person who had a 125 IQ but didn't know nearly as much as I did about what we were talking about even though it was her field. I drew two circles representing scope of consciousness, and said that they were deformable (only area is important) and represented our scope of consciousness.  I made mine smaller, and remarked how this meant she probably would trash me in jeopardy, had a larger vocabulary, was better at recognizing abstract patterns in shapes/numbers etc.  I drew some random dashes and marks all around the circle and outside of it, and said they were memories and ideas.  I said by holding them in the circle she could relate them to each other by metaphor for the use in persuading or amusing others.  I then drew short lines that crossed outside of the circle.  I said that these represented things that she knew were related a certain way by memorization - when she saw one she automatically thought of the other in the correct way.  I drew a small patch of such lines representing her knowledge of mathematics.  She understood all I was saying and agreed for the most part it was a valid metaphor.  Then I went over to my circle and started drawing on it covering up what I was doing.  When I revealed what I had done, the area my circle was in was completely covered by circuitry to the point that you could no longer even see the circle.  Of course in reality my IQ is 140.. but I could have just as easily been having the conversation with someone who had a 160 IQ.  Also, some of that circuitry is geared towards the faster creation of more circuitry so it is far from a perfect metaphor.  But it seemed to get the point across.  Knowledge of epistemology and reasoning skills is not what causes this difference though.  It's about two fundamentally different approaches to dealing with the highest priority human needs.  Most people look to others for security, which basically means they aren't using their intelligence for anything other than mimicking other people's behavior... even if in novel ways.  People who look to themselves for it develop a knowledge base that cascades into what I described. This may even be the cause of IQ increases among a lineage.  Some form of genetic memory is required to explain how our brains evolve with our bodies and even our environments (instinctual fear of snakes for example) But be careful - others learn from memorization of details more than from careful precise generalizations.  They love to point out that you messed up a detail or are not using a conventional labels and use it as an excuse to try and block you out.