You cannot "opt out" of sex education for your child.

While home schooling may be an option or work for some children/parents, it isn't necessarily an option or best for all children.

Many parents don't have the ability to teach higher level classes to their children. I would venture to say the most parents aren't able to teach their children hither level math and science classes.

My son took college algebra in the 10th grade. Then went on to take precal, cal, physics, and other classes that I was not going to relearn from 30 years ago or more. I told him after his college algebra course, he better get it in school because I am done with it. I only helped him a couple of times on concepts, and certainly not actual problems since then.

He had almost a full year of college credits by the time he graduated HS.

He is in his second year of college, and in one more semester he will be a junior, and taking college Cal 2 now. His instructor has his PHD in Physics, and unfortunately after only 2 weeks in school, my son has had to correct his instructor on a couple of problems, because the instructor was working them wrong. I told him to be nice about it, and simply tell the instructor, " I believe if you do it this way, it will work out" Again, nicely. Would he have been at this level of learning had I taught him through high school. Absolutely not, even though I took some of the same classes in college.

Communication is the key. Unless you are going to keep your kids locked up for their entire lives and expect them to never be exposed to immoral things, if you don't have a good line of communication with them, you will never know if they have questions about things, or ask for your guidance or input on things which will come up.

Building a good moral compass is the parents responsibility, but a parent can't be everything, and can't hold the child's hand for their entire life.

It is not only an option for us, but it is by far the best option, in that I am retired, I can devote all of my time to my son, and I have an advanced education in many different subjects, two degrees in history and a master's in business administration (finance).  My son is very, very much aware of the world, and most of our time together is basically "one big discussion" that ranges all over the place, he is 15 and can carry on a conversation worthy of a college graduate already.  While he is not of genius-level intelligence, he takes a very active role in his education, and in the high school years has become very proactive about it, for literature he insisted on reading Crime and Punishment, and after that, he wants to read Xenophon's Anabasis, he came up with that idea all on his own, got it from, yes, a video game.  I'd never heard of the book before.  For sciences and math, admittedly subjects I didn't "double down on" in high school and college --- did well enough, know the basics, enough to teach what I learned myself (I take the approach that, if you set your mind to it, you can learn pretty much anything) --- we do at least as well as students in conventional day schools.  I know the present-day romance is with "STEM" (science, technology, engineering, and mathematics), and that what passes for liberal arts is a kind of afterthought, basically an extended exercise in political correctness --- turn out technocrats who spout the party line (shades of the Soviet Union!) --- but that's not our focus.  Our religion component is traditional Catholic doctrine, Scripture, morality and ethics, augmented by nods to philosophy now and then.  Next year, after we've finished the two years of French, we are going to have a "just enough Latin" one-semester course.  I think he will come out of all this with the end goal of any educational process worthy of the name, and that is how to think. 

If the parents aren't leading a moral life or teaching morals, why would they be worried about whether or not the child is learning morals?   

If the child questions certain beliefs, you explain them to the child.   You also lead by example, and show them instances in the real world of where immoral actions have consequences. 

It isn't a bad thing for a child or adult or whomever to question things.   The problem arises when they would rather question those things to people who shouldn't be giving them the answers because they are wrong.   Again, communication is the key.   If the child doesn't feel like they can ask those questions to their parents, they will look elsewhere.   

I'll give you this earnest tip from a mother with a 31 year old, 30 and 27 years old.  2 remain practicing the faith and to my immense joy, my daughter has a lovely boy who adores her enough to wait for marriage for sex.  My middle one is my work in progress but here is my one tip.  Make your daily prayer a petition for your children's faith and happiness.  Whatever the ups and downs along the way, never give up on that prayer.  Everyday I find myself saying thankyou God and I'm sorry I doubted you in those times I did.  Also, resist being judgmental of others as if you are better then they are.  That is the worst way to form your child's moral compass.  

I am not going to get in an exchange with you over this, but I shall simply answer the questions:

(a) - I have taught him that couples may use it when there are just reasons for not having a child at that time.  This is consonant with the Catechism of the Catholic Church (which I use as a reference).

(b) - This is a question that only the couple themselves can answer, possibly with the assistance of a confessor or spiritual director if they cannot come to a decision themselves.  McHugh and Callan gave four children as a general rule, but the question that then begs to be answered is where they came up with that number.  Their Moral Theology has a 1958 imprimatur, but it is not 1958 anymore, and economic circumstances in much of the world have changed to the point where having four children is more difficult for most people than it was in 1958.  There is no magisterial teaching that prescribes a set number of children.  

I am content to let you think what you want to think, because you're going to do so anyway, regardless of anything I might say.  I owe neither you, nor anyone else, any explanation of why practicing NFP might have been easier for my wife and me, than it might be for some other people.  Not all people have the same ease, or difficulty, following any particular moral teaching.  Pope John XXIII was able to say that he had never committed a sin of impurity in his entire life, whereas St Augustine's difficulties in this area were quite the opposite, and possibly even St Paul had an issue in this regard (his "thorn in the flesh").

You seem to be maintaining that any use of NFP, for whatever reason, is virtuous because of the self-sacrifice it entails.  That is not necessarily true.  NFP can be used for selfish or unworthy motives, a moral means to an otherwise sinful end, just as, hypothetically, artificial contraception could be used for good or praiseworthy motives, an immoral means to an otherwise good end.

As I said, I am not going to get into an exchange with you on this.  I might challenge your ideas, but I have never attacked you personally, and I ask you to consider responding in kind going forward.  On that note, I turn to you the other cheek.