I think the cut throat description is overused and almost interchangeably with “rigorous”when it comes to schools where there is a high academic standard and a very smart and driven student population. It’s generally not a good descriptor and there are always micro environments in every school where there are some students who behave in a “cut throat” manner.
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Of course, what is overwhelmingly rigorous to one student is just right for another.
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I agree the major is really important, but a large portion of the student body arrives on campus undecided. An equally large portion of the student body ends up changing majors during their time at school.
So in those situations, a heavy focus on the major in making a decision of which college to attend may not be a good idea.
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UChicago, Swarthmore, Reed, Carleton, Columbia are known for rigor as well – and since most of their students aren’t majoring in Engineering or CS (which are said to be rigorous everywhere), the reputation likely is due to the overall curricular structure and academic vibe at those places.
Edit: not to impugn the MIT/Caltech rep for being the proverbial firehose aimed at a sipping child. hehe
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I actually considered mentioning Caltech (and even started writing in a parenthetical), but decided against it as to not complicate things, limiting myself by saying “arguably”. 
And my argument is largely based on the fact that our older actually had an IOI winner and a Putnam fellow as his lab mates in one of the classes.
And there aren’t any Putnam fellows at Caltech:
Or ICPC winners:
But, again, this isn’t really meant to throw shade at Caltech. It’s more hardcore in other ways (e.g. its core is hard). Our older was certainly proud of his admission there, and we gave hm this famous mug as a souvenir:
But if one does know one’s major ( common in computer and engineering) it should reassure one that great outcomes can be achieved in those fields from schools well down the ranking list.
MIT does pride itself on its fire hose education:
But our older kept saying he’s still waiting on them to turn up the water pressure (he ended up graduating in 5 semesters).
Again, this isn’t what “cut throat” means. You don’t have to have someone else fail to be successful at MIT. There’s plenty of opportunities there for everyone willing to work hard.
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There used to be a shirt sold at Tech saying “M.I.T. The Georgia Tech of the North”.
In my opinion, these two are very different schools, other than being focused on engineering and being top notch.
Ah, yes, but there can still be a very big difference within the same major.
Some of the opportunities available to top students at top schools aren’t as available to top students at average schools.
That is just the fact of life.
Average outcomes are just that - averages. And there is no such thing as a single event probability. Each student will generally only have one try at an undergraduate education, and in the end, what matters to you is your own outcome.
And you just can’t know it in advance, and so trying to optimize for it is hard.
But some things you can know in advance, and with a good accuracy too.
And in our opinion, the single most important factor is the peer group.
Different schools of thought existed on that for millennia, from Caesar’s “I had rather be the first in a village than the second in Rome” to Pythagoras’ “if you can become an eagle, do not strive to become the first among the jackdaws”.
But no matter where you end up, remember Plutarch’s “it is not the places that grace men, but men the places.”
You still have to do the work.
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That is for sure, given that GaTech is public and has to give priority to Ga Students.
Yes indeed–I ran afoul of this one 30 years ago, when I picked a school sight unseen (vocal performance major, merit aid). 
Interesting in a ranking thread to ponder has anyone ever heard an MIT student claim to attend the Northern Georgia Tech?
Apparently rankings have some influence.
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We relied less on the precise ranking of given set of schools and more on the general range in which those schools tended to fall. A bit like @prezbucky 's tiers approach. We knew the difference between Williams and Knox. That was the bite we took at the whole thing. And it was generally just awareness, so sure on some measure it played an influential role. But as @AustenNut wrote above, it was a data point. I can say categorically that none of my kids would have ever attended a place they didn’t like or at which they couldn’t see themselves, no matter the rank. In fact, I’m positive all of them were admitted to schools typically ranked above the school they chose.
Sitting around navel gazing over rankings is about as far away from each of my children’s personality type as you can get. But each of them, to varying degrees, “fit” many of the characteristics of kids/peers who wind up at highly ranked schools. So given their peer group, which I also believe to be important, yeah, they wound up at fairly highly ranked (T 20) schools.
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Sometimes I get caught up in the excessive compartmentalization (hair-splitting) necessary to create tiers of about 5-10 schools. For instance, in my insanity I have seen fit to put Dartmouth and Yale in different tiers. That is probably ridiculous. So I guess I do it just to see how arbitrarily precise I can be. Also, it beats failing a hard Candy Crush level for the 100th time as a means to combat boredom.
There are hundreds of very good (or at least, impressively adequate) schools in the US. Kids should choose based on fit and finances. If you get into Princeton and it fits you best, and it’s affordable – by all means, go. But if the University of Wisconsin fits you better, and it’s also affordable… there is no shame in choosing it.
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Well, decisions at the margin of each tier is in effect a ranking, subject to all the usual hand wringing. But even tiers require the line to be drawn or there would be but one tier, which helps nothing. 
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Drawing the lines is really hard.
Math competitions are games that MIT highly values, far more than any other institution. I would take it at that and nothing more.
Wow, that is quite a loaded statement right there!
It would take a while to fully unpack, but I will try to be brief and stick to just a couple points.
First, while, yes, most other institutions do, indeed, value ball games over math games (which is a whole different topic), Caltech, thankfully, is not one of those institutions. And IMO-level math talent is as close to a guaranteed admission as one can get anywhere.
So it’s not that many of those kids are at MIT because no one else will take them. Rather, they are at MIT because that is where they want to be, in part because that is where many of their peers want to be. In the battle for cross-admits, MIT wins Caltech 3 times out of 4 (2 out of 3 vs Harvard, 9 out of 10 vs CMU):
But there’s also this other aspect: when you refer to these competitions as games, that is technically correct, I guess, but it somehow seems to sound a bit dismissive, as if they don’t really matter for anything beyond the competitions themselves - yet the lists of both HMMT and CMM sponsors read like a who is who of the companies that are vying for the most advanced mathematical talent (as well as AMS and the schools’ respective math departments):
https://www.hmmt.org/www/about/sponsors
So while most kids involved in these competition do it out of sheer love of the intellectual challenge they provide, these are far from fruitless pursuits, because bringing oneself up to this level of mastery builds the mental muscle in the same way that elite athletics build the physical one, and it serves these kids very well both in and outside the classroom.
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I suppose this is pretty close to my own college decision making process since at the time I was applying, college in the UK was free. I simply picked the most prestigious college at the top ranked university and only applied there. I didn’t think for a moment about “fit”. Even today, the cost in the UK is basically the same wherever you go, so this wouldn’t be atypical for a very well qualified student.
But for my kids in the US, cost (or rather budget) was a more important consideration than rankings. However, rankings were moderately helpful in convincing my kids that even though our instate UCs were cheap, they were better than their affordable (but more expensive) OOS options.
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No, rankings did not matter for either kid and we never considered them.
Neither one of my kids applied to the highest ranking schools that they qualified for (on paper) and neither one of my kids attended the highest ranking school that accepted them. That was not important to them.
We focused on fit, and not all higher ranking schools met their criteria.
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