Because they are. They are not, however, the product of the education that they received at their college, but a product of the branding in which the college has engaged. The professors are really not the ones telling them that “you’re all Harvard students, therefore you’re elite”. It’s the administration who is hammering that into them. That’s how you get Princeton students complaining about the work load claiming “we already have been accepted, why do we have to continue to work hard?” That’s why super wealthy and influential people use their money and influence to get their kids accepted to these colleges.
While universities are “higher education”, education of undergraduates is only a small part of the mission of research universities.
Professors at research Universities, which includes all of the Ivies, BTW, only have 40% of their job as teachers, and only half of that teaching undergraduates. Most tenure-track and tenured faculty at research universities only teach one undergraduate class a semester, at most.
Professors produce the vast majority of the scientific research that is being done in the USA. That affects the well-being of the USA is so many deep and profound ways, and has little to do with what they are teaching their undergraduates.
When we look at education, Professors at all colleges are also producing the next generation of researchers. These, however, are only around 1%-5% of all undergraduate students. Professors also teach courses to graduate students - that’s some 50% of the teaching duties of faculty at Research Universities. This has little effect on the social processes in the USA, but, again, has a profound impact on the well-being of people in the USA.
On the other hand, for the vast majority of students, faculty at all colleges provide an education, which consists mostly of knowledge and some attempts at teaching their students how to analyze data. That has a profound impact on the abilities of that student to perform well in the rest of their life. However, it has very little impact on their politics or ethics.
Universities do affect whether we have vaccines and other medical treatment, whether we have better homes and transportation, healthier food and more affordable clothes, how we affect our environment, etc.
However, while social sciences and humanities have a lot of impact on our understanding of past social processes, they don’t really have that much impact on existing and emerging social processes. College faculty in the USA do NOT determine whether people care about their neighbors, whether they believe in a Deity, whether they prefer socialism or capitalism, whether they want to marry, etc. The reason that many of these movements start on campuses is because those are places where young people with extra time meet and discuss life and other things. Colleges are great places for social movements to spread and evolve, regardless of what is being taught in the classrooms.
BTW, the biggest social movements are not started at the Ivies, nor are they at their most intense at the Ivies. The big political demonstrations are at public universities, and always have been.