I agree that it’s about fit, not public vs private. We did public K-8, private HS, and now public flagship for college.
My kids applied to mixture of private and public. We didn’t encourage one over the other. Money was the main concern and we made it clear from the beginning what we could and could not afford.
We had DS and DD apply to our large instate flagship as well as our local directional, we researched private and OOS schools together, looking for fit, intended major, finances, internships, study abroad, graduation data, course selection, location in the country, etc. Next we toured those that fit within a criteria. For my son, it was a mixture of instate public, military academy, and several small private universities and 2 LAC’s. For my daughter, it was 2 in state public, 3 midsize private universities and 1 LAC. They both ended up at the same LAC with merit and financial that was lower than instate flagship.
As @retiredfarmer said, it behooves everyone to do research (by potential major as well) when it comes to class sizes, what departments/faculty focus on, support, career counseling, etc. And also just what is needed, what special perks/advantages would be taken by a kid (which depends on the kid), etc.
I also see a lot of people making assumptions on this thread.
Many private colleges use TAs, and many private colleges except for the richest ones (that are typically the most difficult to get into) have budget limits (and then you have the Sweet Briars and Hampshires of the private college universer). Private colleges are not automatically better than state colleges in academics, reputation, and internship/job recruiting.
Call him crazy, but our S researched engineering programs. The colleges he applied to, both public and private, all had great engineering programs that met what he was looking for. His final list had 5 privates and 8 publics. The more options - the more better.
@socaldad2002: In our case, applied ED to a Private National University & applied early to two publics with rolling admissions. Was quickly admitted to both large publics. One offered a full tuition & fees plus room & foreign travel scholarship so withdrew the ED supplement to the Private National University. Was admitted to the Private National University RD & chose to attend there.
Reason for selecting the private school was that the primary major was ranked #1 in the nation. However, would have been quite happy at the large public honors college with a full ride plus.
Also considered the three main service academies. No LACs were considered, even though offered admission to one, as attending boarding school made it a “been there, done that” experience in our eyes.
We inherited enough money just before the kids were applying to college that we were unlikely to provide need based aid, but we also now had enough money in the bank to afford colleges for them without taking out loans. The SUNY’s weren’t a particularly good fit for either kid. Oldest was a stellar student who was looking at top CS programs. Younger one was looking for strong IR schools. He wanted to be in or near a city. Older kid looked at Berkley but the OOS cost, the impacted major issues, the lack of housing for sophomores all took it off the list.
For many kids public universities offer a lot, just not mine. 
FWIW they both got merit aid offers at their safety schools.
It’s all about fit. And finances.
Finances may surprise some parents and kids. Students who can get into a “meets full demonstrated need” private college and are eligible for financial aid may get a much better package from that private college and end up paying way less money than they would pay at their state universities. My son has friends at college for whom this was true. Williams was dramatically less expensive for them than their offer from their state uni. Top colleges are so generous that no strong applicant should ever rule them out based on cost without first running the net price calculator.
Fit is individual for each student.
The first criterion for choosing a college named by my child, even before he ever picked up a college guide, looked on a college website, or went on any college tour, was, “I want to go to a college where I’m the dumbest person in the whole place.”
Although this statement was a comic exaggeration, it had a kernel of truth about what he wanted for his college experience. Right then and there, I knew we’d be visiting some elite private colleges, because that would not have been true at even our state’s finest university— where some kids surely are as smart or smarter than he is, but there is definitely a mix. I also knew from his statement that our state universities, and any private colleges that might give him merit aid (by definition because he would be among their top applicants), while still worth visiting and applying to, probably would end up being “safeties,” not top choices, for him. He was seeking a particular type of intellectual environment.
Then, after visiting schools, he refined his criteria further (as detailed in other threads I have posted: “Journey from Clueless to Williams,” parts one, two, and three, and reviews of individual colleges on the thread of “Colleges your child crossed off the list after visiting, schools that moved up on the list. Why?”). So most, but not all, of his choices ended up being very small, private, northeastern liberal arts colleges.
So, my kid did apply to a state university, and was accepted early action… but then he was accepted to his top choice early decision, so that was that. And after his first semester, he stated that his college has exceeded his expectations for college in every way. Music to our ears as parents! It is a good fit for him.
I would also disagree with the term “encouraging”. While there are many threads about the merits and chances of different schools, I have not seen much evidence that parents are encouraging their kids to look at any specific type of school. I also see very few parents who are “choosing colleges for their kids”.
It seems to me that parents are encouraging their kids to choose schools based on finances, fit, and distance from home.
There is also, as @bopper wrote, a lot of self-selection here. Overall, private schools will be more selective than public schools, especially the smaller ones. So people are more likely to ask for advice on the more selective schools. Also, most of the public schools to which people are applying are their in-state schools. This means that they have many other sources of information, like neighbors and friends who went there or the school counselors, who are generally very familiar with the state schools. So people are less likely to come here to ask about the public schools to which their kids are most likely to apply.
there is also the fact that the vast majority of colleges with very low acceptance rates are private. To increase the chance that a kid will be accepted to one of these, they’ll need to apply to a number of them.
Just keep in mind that you are reading posts from a self-selected demographic.
MOST students and parents who are on track to attend their own in-state public options don’t really need this site – or at least are unlikely to be posting in generalized threads about college search & selection, or college admissions. Generally the admissions requirements for in-state publics are pretty straightforward, and public high schools counselors are usually familiar with and informed about those things. And only a handful of public U’s are so selective that students or parents would feel the need for specialized advising to get in. I think you will see some find this site when there are specialized needs or concerns — students applying for audition based arts programs, for example.
But for the typical kids around where I live who attend one the local community college or cal state campuses? Most don’t need what this website and forums are selling — and the ones who do are likely to be seeking that out in both the private and public context. Because why shut the door on private colleges, other than for reasons of distance or affordability?
Was he trying to get you to donate a building to the college that you graduated from which would be an unrealistic reach for him in the absence of development and legacy hooks? 
Ha ha.
As a public school district employee, the only building I could donate would be four inches tall and built out of Legos!
@TheGreyKing: I understand your son’s aim to attend a school where he could grow. We phrase it differently by stating that we don’t want any school where the student would be in the top 10% of admitted students. (We want the student surrounded by bright motivated students who would facilitate growth.)
Interesting, because for many students who need merit aid to afford certain schools , it is very beneficial to go to a college where you would be in the top 10%. In such a case you will still be “surrounded by the bright and motivated.”
That may be the case with large public school honors colleges. And we understand & understood that at the time. However, being surrounded by the bright & the motivated is not a given in that situation. I prefer to avoid a debate, but for simplicity sake would rather Princeton than a state school honors college barring any specific draw to a particular school.
Unless you live in some area that’s lacking decent public universities – or unless you’re a bit of a snob – there is no good reason to apply ONLY to privates.
I wonder if OP is thinking of families who focus on LACs as those tend to be private schools. For example, US News ranking of LACs does not list a public school–outside of military academies–until #90 New College of Florida.
Among the top 20 National Universities as ranked by US News, the only public is #19 UCLA .
Re: #77
Or perhaps it means that the more ranking/prestige sensitive students/parents will focus on private schools.
There are lots of reasons-- both of my girls wanted small schools with a particular feel. There were no state options that met that criteria.