But we are not Ivy League. It's a huge generational (especially East Coast) snobbery that thinks East Coast schools are better. It's embedded in politics, corporations, etc. Rice University in Houston is considered an exceptional school in Texas. It's enrollment is only 6,700 and accepts 14% of the applicants. It will never be considered an Ivy League School.
The main reason BYU won't be considered an Ivy League school is because 1) Mormon and 2) it's too cheap to attend.