Hi OP, I am another one who was, and still am "shy" (I'm 62 in case that is relevant). Does your teenager know that his teacher has said that, if so, does the thought fill him with dread, or even a slight hope that lt may help - he can feel both of course? Regardless of whether your child knows about this comment or not, I would (as politely as possible - I wouldn't be feeling polite) ask her what her qualifications are as a child psychologist, and how much experience she has. Unless she is a fully qualified child psychologist, who also has a child psychiatrist to discuss individual children with, in her team, I would be telling her no, she must do no such thing. I doubt that she is a fully qualified child psychiatrist, as they wouldn't normally just observe a child, and then decide that the child is "quiet", and all they need is bringing out of themselves in the way she describes.
If your son actually does want to feel more confident (I am not saying that he doesn't already, or that he shouldn't feel confident just because he is quiet, but if he doesn't), and/or wants to feel happier to ask more questions, read aloud to others, give presentations etc, then unless this teacher is qualified and has the time and resources to commit to his "therapy", then I think you should maybe consider him seeing an actual child psychologist. There is absolutely nothing wrong with being quiet, but one of my adult children is quiet and shy, and goes bright red when they have to talk to a group at work, and it is hindering them from wanting to go after promotions as a promotion would mean being a team leader, and having to speak both to the people they would be leading in a group situation, and to higher management teams as well. Only you, (your child's other parent?), and your child should be discussing this. Your child's teacher was probably right to flag up a potential problem with your child, but personally I think that should have been done privately to you, not in their school report. lt should be your's, and your child's decision about whether quietness (and any possible reasons for it - it could well be just a trait your child has, and lt can be an endearing one too), is a characteristics that needs to be addressed.
I am sorry this is so long, unfortunately, I have problems trying to express myself more succinctly, and I do think that it is a very important topic. I wish you, and your obviously intelligent and lovely son all the best in the future.