AOs are looking for a diverse student body.
IVYs admit fewer science and engineering students. Plus those students may not fit into the drinking, party environment. (check Evan Chen, who transfered from H to M, and read his story if your son/daughter is a science/engineering student)
IVYs teach students to fit into society and make changes. MIT lets you to find yourself.
If the child majors in social sciences, by all means go to IVYs, even though M has very good programs as well. They probably enjoy IVYs more.
M has more than 20(?) departments. So it would only take the top math students. It is one department only.
# count for USAMO is ??