I ran into trouble with this as a kid. They put me ahead a grade in math in grade 2 because I could handle it and the class was a 2/3 split (half grade 2s, half 3s), so I just did math with the grade 3s. This worked going forward as there were 3/4 and 4/5 split classes at the school too.
But then after a couple years, I was reaching the point where the school only went to grade 5 and the teachers didn't even have books for grade 6s.
So they skipped me entirely ahead a grade. Into a new school (since the previous school only went to 5). With none of my friends.
My other subjects suffered because I was only really good at math. My social life died- kids are assholes at that age and pull each other down. And my mental health was pretty messed up for a long time. I wound up taking an extra year of high school just so I wouldn't be in college at 17.
The second reason was that if I had graduated on time, it was a bad year to do it. The province was phasing out 'grade 13', called OAC[0], which had existed for decades as an optional pre-university year for students in high school. It was the last year it existed, so there would be almost twice as many students vying for places in post-secondary schools. Why compete when I could be lazy and have an easier time?
- There is no depth in math without understanding properly our own language.
- One cannot master anything without actually writing stuff.
My children attend a school district where the norm is enrolling kids in after-school math programs. According to the standardized tests run by the school, about 50% of the students are pacing a full grade ahead.
The school does offer an option to skip a grade in math, but the pass rate is a mere 10%. While the skip test covers the standard material, it does so with trickier questions, tripping up many students. They're moving fast, but without much depth.
What I found works best is to pick a challenging and exciting curriculum that allows talented students to immerse themselves and experience the excitement and satisfaction of intellectual discovery. There are a few examples of such programs. The most popular of which is the curriculum offered by AoPS (art of problem solving), which starts at first grade. Following this path naturally offers a large advantage to learning at the highest levels. If they are still moving faster with the rigorous curriculum - sure, let them accelerate.