More detailed answers:
First, not all of these numbers actually deviate from what is expected. Unless there are a good number of applicants, it is difficult to say much about acceptance rates. An 5% average acceptance rate doesn’t mean that, if 20 kids from a high school apply, 1 will certainly be accepted. Moreover, the average acceptance rate of non-hooked applicants to a colleges with an average rate of 7% is around 1%-3%.
However, it is also often an actual pattern for colleges with a wide ranges of acceptance rates.
Some of these numbers also have to do with the population of a given high school. If your kid is attending a high school which does not have a substantial number of legacies or kids from very wealthy families, acceptance rates to colleges where these are important factors will be low.
And indeed, local reputations is important, and there are often connections between GCs and AOs at some colleges as well.
So, while the percent of kids who were accepted from my own kid’s high school to Harvard, Yale, and Stanford matched what would be expected, and acceptance rates to Cornell were higher than expected, Princeton has not accepted an applicant from my kid’s high school in the past decade or so.
Conversely, my kid’s high school is in Chicagoland, and acceptance rates to U Chicago and Northwestern are far higher than the average acceptance rates to these schools, because of connections between the school’s GCs and the AOs of these schools, and because of the local reputation of the high school.
This also affect admissions to colleges with higher acceptance rates. So, for the same stats, a student from my kid’s high school is much more likely to be accepted to Carleton, WashU, Macalester, UMN, UIUC, St. Olaf’s, and a host of other Midwestern colleges than the average acceptance rates to these colleges by students with these stats.
On the other hand, I cannot say anything about acceptance rates to Brown, UPenn, Dartmouth, and other East and West Coast colleges with low acceptance rates, since the number of applicants to these schools is too low for any meaningful analysis.
Sometimes issues of legacy and religious or political background can have an effect on both applications and admissions. So very few students from my kid’s high school apply to Notre Dame, despite the fact that it is pretty near (nearer than WashU, for certain).
All that being said, the only way that a student is certain to never attend a college is by not applying. As the old joke goes - a man who has been praying for years to win big in the lottery and hasn’t, rails about his prayers not being answered, and God suddenly speaks to him, saying, “WORK WITH ME ON THIS, BUY A TICKET!”.