Yale has a graduate School of Drama and has always had a good reputation in drama and other performing arts.
My father remembered that Broadway plays in development would often go to New Haven for pre-Broadway shakedown performances.
A friend of mine went to Harvard and mentioned that when Harvard was losing against a team from another Ivy school, they would chant:
“That’s alright,
That’s okay,
You’re going to work for us someday!”
Did not endear them. 
Same at Northwestern, except the last line was “you’ll all work for us someday!”
This is 100% true, but not a trick, just human nature. In a world where education can be obtained in an ever wider variety of ways, nothing has changed about shared experiences and networking. And quality time with subject-matter experts at the top of their fields, from the full-time academics to the industry leaders and subject experts giving guest lectures in classes every week of the term.
As Mav said in Top Gun, it’s a target rich environment.
The safety school stuff is garbage, but will always persist due to the same human nature. You hope you’ve given your kid a bit of perspective. If you have to say “don’t be a douchebag, son” as they are leaving for school, you may have waited a bit too long.
“Where did you go to school?”
“Yale.”
“What’s your name?”
“Yohnson.”
Yalies are often portrayed as boorish in popular culture.
Same at scores of schools everywhere. There are no pair of schools anywhere where one group of students isn’t looking down on the other, most of the time it’s both simultaneously.
Consider, for example, Aggies jokes that are told at the University of Texas. I had never thought about whether there are Longhorns jokes that are told at Texas A & M University. I just Googled on it, and, yes, there are. Also, Thurston Howell III is identified as being a Harvard graduate in Gilligan’s Island. Presumably if he had been a Yale graduate, he would have regularly insulted Harvard graduates.
Brown? We got one of those in Providence.
I turned down a tenure-track position at Yale about a dozen years ago. So that’s one less famous person 
Emphasis added. You misspelled “most” (and in some years “all”). 
Montgomery Burns
And Richard Gilmore.
Who is now having a residential college there renamed after her: Yale changes Calhoun College’s name to honor Grace Murray Hopper | YaleNews
Which is nice, but it’s not like, y’know, getting a *destroyer *named after you: USS Hopper - Wikipedia
Actually, the first use of the term Ivy referred to those eight and West Point.