There are two potential issues that come up when a student skips a grade. If they do this before high school the main issue is that the student will graduate at a younger age than their fellow classmates. Selective colleges in general, and BS/MD programs specifically, have concerns about younger students entering college. Why?
Younger students are often less mature than their classmates. Less maturity often leads to students doing stupid things like binge drinking. Yes, older students do stupid things like this also, but the chances increase with less maturity.
For BS/MD programs, maturity is a huge issue because most 17 and 18 year old students aren’t mature enough to choose a profession for the rest of their lives. Less mature students may not fully understand what they are getting into and eventually drop out of a program. BS/MD programs try to avoid drop outs as much as possible.
So much of the application process for BS/MD programs addresses issues related to maturity. When a student is applying as a 15 or 16 year old, those concerns are magnified.
The second issue that occurs if the grade skipping occurs in high school is that the student generally no longer has 4 years of each of the core subjects. Since most people applying to selective colleges and BS/MD programs will have at least 4 years of each of the core subjects, the student who skips a grade may be at a disadvantage.
I understand that sometimes there are few options for advanced students other than skipping a grade. However, it is not a decision to make lightly. Before making that decision see if there are classes at local colleges that might be able to provide advanced classes or even online programs through colleges around the country.
You might be doing yourself a favor in the long run by not skipping a year or two of school.