I'm going to perhaps go against the grain here...
I honestly feel like you deserve more of an answer than "he's not ready yet." What (relatively) specifically does he need to work on? What can you do to help him improve? What is their assessment criteria?
I'm a school teacher. I know it's not an apples to apples comparison, but there's some crossover (or at least should be) - I'd never suggest holding a student back and simply say "he's not ready yet" and walk away. Forget educational laws and regulations, I feel personally obligated to tell the parents what their kid's strengths and weaknesses are, and how they can help their kid improve whenever asked.
You're obviously confused and frustrated by this. Completely understandable. And even more understandable for your son to be. My advice is make an appointment with the chief instructor/owner and ask him/her what's going on professionally and politely. And in private. You are a paying customer and you're entitled to a professional explanation.
None of that means you're entitled to the answer you want to hear, nor should you have the "I pay your salary" mentality. It just means you deserve an honest answer. You can either accept the answer and follow whatever is recommended, or you can leave and look for another place. But you can't make the rules.
My dojo has the rule of don't ask to promote too. But that doesn't mean I can't ask my teacher what I need to work on. If I couldn't ask my teacher what he thinks I need to do to get better, I'd find another teacher. If I regularly wasn't invited to test, I'd ask him privately what I need to do to move forward. If he didn't want to answer that, I'd leave.
But remember, there's a way to ask. Don't come off as a jerk and you deserve the CI's honest assessment.