I don't have an ax to grind against the concept of school in general. There are good ones and there are bad ones. There are good teachers and there are bad teachers. There are also schools and teachers that are good for some kids and not good for other kids. Education is not a one size fits all sort of thing. The thing that I do have an ax to grind against is the idea that all children need to be educated in one specific way. That idea is patently ludicrous and isn't even borne out in the world of public education within one given system, much less across the many different systems that exist on our planet today.
Some people think that you can't give your child as many opportunities to learn at home as you can in a school environment, and for some schools that may, in fact, be true. The vast majority of schools, however, suffer from the opposite problem. Each class has to teach to a specific level, not getting ahead of itself for the quick nor slowing down for the laggers. Most schools suffer from a lack of funds and resources, and so they have to do with whatever they have. In general, schools also suffer from time constraints that require subjects to be carved into specific time slots and attention blocks.
At home you are not constrained by the four walls of an institution nor by the scheduling issues of a corporate body. If you would like to study French by visiting a French speaking place on the off season, you can go right ahead and do that. If you would like to keep reading your book about Greek history past 10 o'clock at night, that's fine, too, as long as your own priorities for the next morning allow for a late wake up.
As a homeschooler, for each topic you study you can be an autodidact or you can seek out tutors from a wide variety of sources. Sometimes you will choose to take an organized class on a specific subject. Sometimes you will find an inspiring mentor to help guide you in a particular learning endeavor. Many times you will learn a single subject from a number of different people that you communicate with in different places and different contexts -- the librarian, a professional in the field, hobbyists on the 'Net, friends you meet at a supply store or event. Some of your teachers will be peers of your own age. Some of your peers in a topic you explore will be much older than you are, and will be learning as much from you as you do from them.
As a homeschooling parent I don't have to know everything that my children want to or need to learn. I never even took calculus, so how could I ever teach it? I can't. Instead, my kids can teach me, or we can learn together. I take immense pride in the fact that my eldest son taught me almost everything I know about marine biology and absolutely everything I know about cephalopods in particular.
Homeschooling builds a sort of tightly bonded family that is extremely rare today in the Western world. People notice the relationship that I have with my kids, and fellow homeschooling families say that they experience the same thing. One of the reasons that we are so close is that we talk to each other. A lot. About lots of different subjects. That builds familiarity, sure, but it also builds trust. How many teenage kids actually enjoy sitting and talking with their parents? For me, the teen years have proven to be the best so far precisely because of the great conversations, movies, books, and activities that we've been able to share.
Homeschooling also builds a kind of independence that is uncommon amongst regular-schooled kids. The homeschooled youth knows that he or she has power over their day, their life, and the things that they learn and do. They may be guided by adults, but they have a much stronger sense than most about the fact that they are ultimately in control. Whereas school children who study topics outside of the school curriculum or skip ahead in their textbooks are considered nerds and geeks, homschooled children who do the same are the norm. Whereas school children who decide to start their own business, write a novel, arrange an apprenticeship for themselves or volunteer independently at an organization they care about are considered remarkable, amongst homeschoolers any of those endeavors are just part of the package.
I love homeschooling because it is limitless, borderless, boundaryless, and immensely fulfilling.
When I was very young and impressionable, somewhere around the age of 6 or 7, my dad told me that school wasn't there to teach me all the subjects that I was supposedly learning. What it was really doing was teaching me how to learn. Learning, he said, is one of the most important things in life. You will need to do it all the time if you want to be able to compete in the job market, if you want to be able to keep up with changes in technology and science, and if you just want to be a better person. Reading and math are tools for learning. The scientific method is a tool for learning. The things you learn about social studies and literature are building blocks on which to build more learning.
The thing is, if that's true, then school may be the wrong tool for teaching what we most need. What percentage of 5 and 6 year olds start their school careers as curious and inquisitive little beings excited about the prospects of learning more, more, more? What percentage of people come out of school full of wonder and a desire to keep learning? I don't have exact numbers, but I'm sure that you know as well as I do that the majority of people finish up school feeling burnt out and not wanting to go back to that experience ever again. For many people, the idea of learning a brand new skill 5 or 10 years after they have gotten out of school is terrifying. This does not bode well.
There are a few things that I think that my parents did extremely well in my early life. One of them is that they helped me to separate between the concept of "school" and the concept of "education". When I was a kid the first was presented to me as a legal requirement, the second as a thing of great joy which, when you are lucky, you can glean from the first. Why hope for luck when you can squeeze education out of every moment in your day without school?