You've gotten excellent advice above. And your son did the first thing many on here would have advised - talk to the coach himself.
Nearly all of us on here have experienced what you have in one way or another. Might've been an all-star coach, or a travel coach...or another HS coach. As pointed out above, even the very best professional baseball players find themselves in confusing situations not too different from this one more than once in their career.
Keep in mind that most private instructors, if paid by you, will tell you wonderful things about your son. For one, they nearly all believe they can help...they are optimists as they should be! But they also want to build a relationship with you and your son. A good relationship gives them a better shot at helping your son and they want you to come back (and keep paying them).
Whats the good news? HS season ends soon. Summer will be upon us and if you find the right summer team - your son will re-find the joy of playing baseball. We went through some of this with our older son. As a freshman in HS, his coach f-bombed him over and over in front of the team and a year later his varsity coach as a sophomore called me and threatened that he'd never pitch in his program again if he took one more pitching lesson all while acknowledging he was the best pitcher in his program.
Sometimes these things take care of themselves (both coaches were removed cause I guess the AD saw the same things we did)...sometimes they do not. But your son does have a real-life situation right in front of him and I believe your role is much more about mentoring him/guiding him through it as he grows into a young man. You can better prepare him for life than baseball here if you take on the challenge constructively.
Terrific opportunity for you as a parent - do your best to take advantage of it. 