The video I posted earlier explains this much more eloquently than I will (and with a lot more statistics), but I’ll give it my best go.
If I’m the at the top of my class (at any school) I’m going to be a front runner for certain opportunities. If I’m majoring in the sciences, that could be extensive lab time as an undergraduate. If I’m majoring in the humanities, it could be working directly with a professor on research he or she is doing. If I’m an engineering major, it could be a big project that the department is taking on. Y’all get where I’m going with this. Top opportunities come to top students.
Now, if I’m choosing between Princeton and UConn, I’m likely a pretty smart cookie. Think about all of the kids who go to Princeton each year that would be the top students in their respective majors at a vast majority of other schools around the country. So if I’m looking at this as a science major, Princeton and UConn both have a finite amount of lab opportunities for me to get as an undergrad (especially as an underclassman). I’m a good student at Princeton, but not a top student so I don’t get a lab position until I’m a senior. At UConn, I could have earned a similar position as a sophomore because I’m at the top of my class.
Now, it’s time for work or graduate school. UConn me has good test scores, a really high GPA, and three years of lab experience. Princeton me also has good test scores, a not quite as high but still good GPA, and one year of lab experience.
This is just one example, but there are a lot of reasons to choose top schools, but just as many, if not more, to choose a different path.