I'm friends with an elementary-grade teacher at just such an institution. The answer in that instance is that the school runs K-12, and is a traditional feeder school for a major ivy-league school. Kids that go there for high school have a much better than average shot at getting in to Big Ivy, but it's mind-bogglingly competitive to even get into the high school there. if you can get them into the lower school, though, they're in automatically. Those parents are basically buying a better shot at the right college.

But this school only accept new students at certain grades, and only a very limited number in most of those. The only point where parents have a more-or-less even shot amongst other prospective parents is in Kindergarten, when every student is brand new to the school.

So basically, get them in for Kindergarten, and little Caden or Kayleigh has a solid shot at an Ivy. Not every school is the same, of course, but the principle remains basically the same: those parents are trying to set up an educational pedigree that will grease the wheels when it comes time to apply to college.