My sons coach is great, he's actually a head coach at a junior college, but he's not a pitcher. I wouldn't want him tweaking my sons pitching mechanics any more than he would want to try.
In the world of baseball there are pitchers and positions players. You can turn a first basemen into an outfielder, shift the guy at third to SS if he's quick, but you can't just grab the LF guy and put him on the mound and expect good things to happen. It's a craft, it's a specialty, and pitchers have their own instructors because of that.
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Agree with CaCo, pitching is much more of a specialty and those with aspirations beyond HS (and often to excel in HS) tend to have their own instructors. A big factor - it is quite difficult to provide regular bullpens for all P's with sufficient individual attention in a team environment (which generally has to occur within the time constraints of the full team practice).
If you are part of a travel organization that has ties to facilities, then pitching instruction becomes a key part of the equation. Otherwise, your move to have him work with a P coach is a good one, provided his personality, philosophy and mechanics are a good match for your son.
As far as quitting on hitting, the only thing I can add to others' comments is that the further he takes his hitting, the more he will understand hitters at a higher level and, thus, can use that knowledge to be a more effective P. But, if he just plain doesn't like hitting, that can be overcome. I will say that it is quite unusual for a baseball player to demonstrate a dislike for hitting at that early age. I know of very few players who have gone on to play beyond HS who were not at least decent hitters in HS. I know MANY who were stuck behind better hitters and smartly made the move to focus on pitching, but none that didn't WANT to hit.