One of the things I like most about homeschooling is that it fosters an environment in which learning happens naturally as a consequence of daily life rather than being something that is imposed on unwilling brains.
To demonstrate: a few days ago my daughter was writing at the dining room table when she looked up at me and asked how one knows whether to use "fewer" or "less" when referring to quantity. I was reminded of my years as a public school teacher, years during which I might spend an entire mini-lesson on such a concept, first defining the words and presenting examples and then having my students complete some sort of follow-up worksheet in which they chose the correct word or made up sentences of their own. Then I recalled how the very same students would turn right around the next day and incorrectly use one of those very words in their own writing (sometimes after "acing" the worksheet).
On this day I answered my daughter's question ("fewer" is to be used for things that can be enumerated, such as "fewer ice cream cones," whereas "less" is for collective amounts, as in "less ice cream"), and she immediately grasped the concept and applied it to the writing task before her. And I know that because that lesson was something that was initiated by her and that she cared about, the learning that took place will stay with her from here on out.
This brings me to what I think is one of the inherent problems with the traditional school paradigm: systemization.* As it attempts to cover all the bases by defining and codifying what the high school graduate should know, it sucks much of the joy and spontaneity from the learning process. Thus, students find themselves being force-fed information that they personally see no need to master and about which they have no curiosity.
As a homeschooler I am often asked "but how do you know that your children are getting everything that they need? How can you be sure that you are covering it all?"
My answer is that I don't and I can't. But I am comfortable with that because I don't think traditional schools can claim to be doing it either. And when I look at my children and see how much they desire and seek out knowledge, and I witness their love of reading and their joy at sharing the things they have learned, I know that my husband and I have made the right decision. I also know without a doubt that while there are certainly gaps in my children's knowledge (as there are in my own and in that of everyone I know--except maybe my husband!), they are capable of filling in those gaps because they can receive and process and think critically about the enormous volume of information that is available to them. And in the 21st century world, where information grows exponentially by the second, I think that is about the best one can hope for.
*I am dumbfounded whenever I see those lists of learning objectives--outlined to the fifth or sixth degree--that today's public school teachers are supposed to meet. I thought they were bad enough when I was teaching school. But like the very information that they are trying to sort and classify, they have grown exponentially over the years. No wonder both student and teacher burnout are also on the rise.