A common question we get is whether it matters where you go to high school.
A strong high school, private or public, that sends most of its students to four year colleges and a significant number to highly competitive colleges would certainly seem to be the best option to get into a BS/MD program when compared to a mediocre local high school. The stronger school will often have advanced classes and it is typically much more competitive to get good grades. And therein lies the problem.
BS/MD programs are very driven, at least initially, to consider students with high grades and test scores. You might be a strong student that at a more competitive school have grades that put you in the top 20% of the class. If you were at a less rigorous school you might have been near the top of the class. In this scenario, you are better off at the less competitive high school getting better grades and being ranked higher in the class.
If you are at the top of your class at a very competitive high school there will be some small benefit when compared to the less competitive high school because colleges often know how competitive a high school is. But unless you are at the top of your class at that stronger high school, you may not even be considered for the BS/MD program.
If there is any concern that you might not be near the top of your class, you need to consider the less rigorous high school as a potential option if you are interested in BS/MD programs. The biggest issue in evaluating a less rigorous high school is whether it has a sufficient number of AP classes. As long as there is at least one in most subjects you should be fine.