Though we have a little perfectionist on our hands, we have not witnessed any negativity beyond the "I am no good at piano" crying fits and the occasional throwing of music books. So, your son's feelings are not normal (at least from what I have witnessed raising my one child) and you are wise to look into the root cause of it.
As for piano - I first try to react calmly to the perfectionist meltdowns (took me a while to learn that!). I ask my son to stop what he is doing and take an immediate break. Then, I ask him to show me where the problems are. I then act as a coach and walk him through the difficult part step by step. This involves reading the notes aloud, checking the finger numbers, clapping the rhythm, playing only the right hand part of the difficult measures until it sounds right and then helping to put both hand parts together. It takes a while, but when I am done, he has usually mastered the difficult part and is happily playing the piece again. The problem with my DS is that he thinks that he is very good at what he is doing and he is used to everything coming easily to him that it is a shock and a major frustration when things don't click into place on the first attempt. I try to teach him to play slowly at first and then pick up speed and he knows the process of working through the difficult parts, but his brain refuses to think logically when he is having the meltdowns and he needs patient reminders every single time.
Good luck and hope you get a handle on the perfectionist meltdowns.
