The short answer without personally knowing your son is...hold him back.
Couple of questions though...is he your oldest child?
In our area..this is very common. My son is a January b-day and he seemed to be right in the middle..he was ready academically and socially. I thought that the parents who held their sons back were babying their boys and it did not make sense to me.
Now my son is in the 7th grade..he JUST turned 13...many of the guys in his class turned 13 last summer and there are some kids who just had their 12th birthdays...
This span in age is gigantic! Some guys are shaving already...their hormones are going crazy...and the same with the girls.
If you wait to enter your son...he will have the additional maturity to deal with all of this other stuff that, if they are stressed out about...will definitely affect their academics.
My husband skipped a whole grade and was the only one not driving when all of the others were...but he was academically brilliant and his father was a pe teacher so he played a lot of sports well.
There are many ways to challenge your son outside of school...maybe a year out and go to Montessori?
I recommend HIGHLY the following books:
"Bringing our boys thru the second decade", Kathleen Fischer
"A fine young man" by Michael Gurian
I think that it would be helpful to take a look ahead and see what issues you will be facing.
If your husband is a very strong male and your son spends a lot of time with family and greandparents and is otherwise very well rounded...it may be okay.
What is the school advising?
C. in California