Prep schools are most certainly better (on average) at teaching students to be assertive, seek out opportunities, bend rules, etc. The coursework is harder and more engaging than even top-track classes at good public high schools. On average students get more individual attention from teachers.
Likewise, there is a wide gap between work difficulty and quantity and expected levels of preparation at top tier colleges vs. average colleges. At top tier colleges, the typical student is incredibly ambitious, and there is a categorical difference between the extent to which typical students seek leadership opportunities and pursue impressive goals. (This is not to diminish the work of typical students at average schools, many of whom come from difficult circumstances and must struggle to pay the bills, etc. And of course there are some amazingly ambitious and talented students even at mediocre schools who do amazing work.)
There are surely still many problems with even the best schools, but the difference is by no means limited to professional networks.
These schools are factories for CEOs and politicians. They have the absolute best teaching, the best resources, a culture that not only encourages high achievement but expects it. If an Etonian or Harrovian says that he wants to be Prime Minister, nobody bats an eyelid - the odds are fairly good that he might well be.
So I will give the opposite advice: Rebel. Be a pain. Skip class. Don't get into college.
If you're unlucky that might close lots of career gates, but at least you got your sanity, and that's the most important thing. A healthy mind is worth a bunch.
Some people can intuitively do division in their head for simple problems, but if they don't learn the mechanical algorithm for it, they are unable to do more complex division.
BTW, I've implemented divide routines in assembler before CPUs had a divide instruction. I used the same algorithm I learned in 3rd grade. Polynomial division also uses the same algorithm.
There is a point to learning an algorithm, even if you already know the answer.
Bingo.
There has been much improvement in curriculum over the years, certainly, but the structure of the American school system is still basically the same one that was originally designed expressly to produce a body of conforming and obedient factory workers with a consistent and predicable level of skills.
* Do most of your homework and get acceptable grades. This is what most students do.
* Don't do jack and be consistent. Many teachers will give up if you never do homework, and if you skip enough classes there won't be enough time to sit out all your due detention. It's also well possible that your school has a leaky detention administration and it ends up never happening.
I found US public school education was not about learning and mastery. It's about conformity and obedience. Learning the subject matter is secondary--the key to succeeding at this institution is to do things in the expected way, at the expected pace, even if it is mind-numbingly verbose and slow. It's a hack: You learn the expectations and do the bare minimum of what is precisely expected, because both less than and greater than the bare minimum will be penalized. I had a rough time in school until I grokked this hack.
Do your homework. It's easy of course, just takes a long time to do since so much gets assigned. The point of doing homework is not to learn, it's to show obedience--you were told to do the homework and you did it.
Show your work. It doesn't matter if you can do division in your head, kid. You're expected to write down the specified intermediate steps so just turn your brain off and do it. The point is to follow the prescribed process, not to master the subject.
Class participation. This is a gift to the outgoing/popular/sports kids to inflate their grades. Just figure out how many times you need to say something in order to get full credit, then raise your hand and say something (anything, it usually doesn't matter) that amount of times.
Public schooling is a series of hoops that you need to jump through at no slower or faster than the prescribed pace. The smart kids figure this out. The REALLY smart kids tend not to figure it out unfortunately.