I think this answer is great because it points out not just the common conception that it opens up an elite social circle, but that it opens up a student's eyes and mind towards what is even possible and what resources are available.
Answer by Jessica Su:
Every accomplished person I know had a mentor. Usually their parents, sometimes teachers or friends. Kids don't just start thinking "I want to go to MIT in 4 years, so I'd better start doing math contests, and getting research internships, and self-studying AP classes so I can take tests my school doesn't offer." Someone had to tell them those things existed, and that they could actually do them.
Similarly, most kids don't think "I want to go work at a trading firm" or "I'm going to intern at Google my freshman year" until they go to a top school and see what their classmates are doing, and realize they can do the same things. This alone gives kids from top schools a huge advantage in the job market.