The simple answer to the playing time riddle is that Coaches play kids that they believe can help them win. Period. This applies not only at the HS level but also college .
That being said , if a kid in fact believes he can help his team win and the Coach sees it differently , the player ( never the parent ) needs to speak to the coach . He needs to be direct and ask the Coach what it's gonna take for him to play or move up to Varsity in this case. At this point most coaches are pretty straight forward in explaining to a player what he needs to do or what the coach needs from him to advance .
It's pretty simple. But most HS kids are afraid to approach the coach. That is sort of a developmental thing at that age. But if he's truly unhappy or unclear about his role or future he needs to start there.
Don't let your son or yourself get caught up in the age old excuse of 'The Coach just doesn't like me' . That is a mistake and will just cloud your judgment . Because it's irrelevant. Remember , HS Coaches play the kids that can help them win. Period. They have 16-21 guys on Varsity , of those 16-21 guys , sure there may be a couple kids he likes personally more than others and occasionally a dislike and more often than not indifference towards some players, but it will rarely change how he makes out his line up card.
A bad student, bad attitude jerk that touches 88-90 mph will pitch at the HS level regardless of the coaches personal opinion of him. Don't forget that.
Have your son talk to the coach about what it's gonna take to advance in the program. After the meeting sit down with your son and put together a plan to accomplish those goals. Then have him go back to the coach once your son has improved in those areas and Hold the coach to his word.