For me, the emotional and mental maturity & development of a child, is more important.
Your son basically skipped a grade.
ULTIMATELY, it is the Parent, that decides. And you then tell the school, what you want for your child.
Keep in mind, that from 2nd grade to 3rd grade, there is a BIG jump, in complexity of the school work, and in the development of the kids. And in expectations... academically and socially/emotionally.
Even my daughter's Teachers said that.
2nd grade, is nothing like 3rd Grade.
I saw that with my daughter. Who is now in 3rd grade.
My Daughter's Teacher said, 3rd grade is no longer primary school. It is secondary schooling... in terms of the academics and social/emotional interactions.
Then, from 3rd grade to 4th grade, it takes ANOTHER leap, in expectations academically and in the social/emotional expectations of a child. BIG difference, between 3rd and 4th grade.
Next, MOST schools have a gifted and talented program. So academically, your son can be in that. Since he is academically, ahead.
Next, you can also work with him, on personal and emotional aspects. Teaching him on how to have self-assurance, to be proud of WHO he is, to speak up and express himself, how to ask for help from a teacher, To SPEAK up when other kids pick on him etc. How to choose friends. How to be himself etc. ie: helping him, gain.... his sense of self and confidence.
IF kids are picking on him, ie: bullying, you NEED to tell the Teacher.
That is what I do. A child, needs to learn, via their parents and how they handle it... HOW to cope and HOW to correct, situations like that. Thereby teaching them, how not to be a 'victim' or think that they have to put up with it.
That is what a Teacher is there for. They will not necessarily know, if kids are picking on another kid, unless a parent or the child, speaks up about it.
That is what my Daughter's Teacher said. She said, to ALWAYS tell her, when things like this are occurring. She then, speaks to the ENTIRE class about it, and the instigating child, about it. She teaches the children, about behavior and what is INappropriate.