There is a difference between wanting to do one's best, and perfectionism.

Doing one's best may involve getting halfway through a project, realizing you've learned so much that you can easily critique your initial work up to this point, and wanting to start over or at least polish up your work a bit (depending upon the amount of time available). This is a healthy, vulnerable, flexible way of thinking.

Perfectionism may involve getting halfway through a project, realizing you've learned so much that you can easily critique your initial work up to this point, and becoming angry, frustrated, down on one's self, calling one's self stupid, deriding one's self, exploding... or perfectionism may involve freezing with procrastination to avoid reaching the point of making mistakes, because one does not yet have the tools to deal with their mistakes in a positive way. These are unhealthy, walled-off, isolated, inflexible ways of thinking, and may be intertwined with a person's unrealistic view of themselves, a negative view of mistakes, and/or a fragile concept of one's identity as "smart": Gifted kids may stop taking appropriate risks in order to always be "right" or always be seen as "smart" or never be "wrong", and this may work against them as a fixed mindset and lack of resilience.

There are books which address the dangers of perfectionism, highlight how it does not serve one well, and help provide seeds for changes in one's thinking. People can learn to acknowledge their mistakes, take them in stride, learn from them, correct them, realizing that much of life is a reiterative process and that mistakes do not diminish us. Link to old post with good article.

If nothing can talk your son out of valuing perfectionism...
possibly he could be talked into valuing being perfectly resilient?