I think some of the most important things we teach students in school have little to do with academics. That is one of my concerns about homeschooling. Where will those students learn the skills they need to be successful in society as a whole?
Some things are obvious: work habits, getting to class on time with the materials you need, or the simple act of showing up on a regular basis.
Other skills can be more ambiguous: working as part of a group, learning to be polite and respectful, and acknowledging authority.
Some students come to school understanding that adults are in charge for a reason - the greater good for all. Others come defiant, leary of all authority figures, determined to make their own rules in every given situation. These are the kids who constantly have to be asked to remove their hat, day after day, hour after hour. They have to be reminded to not speak when the teacher is talking, don't bother other students, ask and answer questions or give comments respectfully.
Through the years, I've had a multitude of students who are unwilling or unable to follow the basic rules of school. Many of these, I've encountered later in life. They are struggling to hold a job, even at McDonald's. One young man didn't understand why HE had to wear the same uniform as everyone else. He got angry and threw his uniform in the garbage, and ultimately lost his job. Others find that employers are much stricter with their tardy policy than the school was. Others find that employers expect you to show up at the job with the necessary tools you need for that particular job and without them, you no longer have a job.
Other students lack skills to interact with others politely and respectfully. They are constantly making comments to their teachers and other students, interjecting little jibes here and there that make everyone's life miserable. When confronted, they claim they didn't mean it, didn't mean anything by it, or flat out deny they even said it. Unless they change their ways, these students will also struggle in the work force.
I think schools need to spend more time and effort on these issues. Too many students come from homes where these skills are not valued. We must teach them. Someday, it may not matter if they can balance an equation, understand the influences the Romans had on our government, or be able to dissect a frog. But it will certainly matter if they can hold a job, be a productive member of society, and understand the social mores of our groups.