Your son sounds like a wonderful child who possesses many positive traits. As a parent, you must be very proud that he is in the gifted program at his school.
It sounds like your son’s frustration may stem from his inability to succeed at everything he tries. As adults, we realize that this is an unrealistic expectation, but children don't have our experience and knowledge. He may also have a tendency to get embarrassed easily because of his age.
You didn't mention how he reacted when he chose not to continue to skate. If he chose to act out, it would be wise to give him consequences.
Try to find a neutral time to talk with him about the reasons why it's natural to fail at things occasionally. Relate some of your own life experiences. Help him understand that it's normal to feel disappointed or embarrassed for awhile when we fail, but we need to pick ourselves back up and try again.