The trend for home educating is , in my view, and on the whole, a step backwards. A return to the days where children were educated in the often narrow and limited views of the parent. Where they were closeted, unsocialised and given little experience of different cultures, social groups and unexposed to different viewpoints. Some parents will educate their children adequately, others won't, and some will use it as a way to hide abuse, push eccentric views on their children and as a tool for shielding their children for enlightenment.
State education, however flawed, strives to give children an equal opportunity. By offering a relatively broad curriculum it provides children with the chance to develop a beginning interest in a particular field. For most, GCSE choices are pretty limited so that they don't specialise too young before they have really developed an interest in a particular area. I think it's important that children continue a broad and balanced curriculum until at least 16.
Saying I've never needed to use algebra since I left school is just a stupid thing to say- it's the sort of thing I hear teenagers say when arguing about why they need to study it. The point is, if you never learnt it then you wouldn't know if it was something you had an aptitude or interest for. And we do a actually use algebra every day, how do you think you calculate the time time a journey takes, or the time required to cook a chicken? Alternatively, it doesn't matter what you are studying at GCSE- whatever you choose, you are developing the ability to study to greater depth, training your brain in the art of learning: how to retain information, recall it, reason about it, problem solve and apply knowledge. Even if you change path in later life and never return to the subjects you studied at school, the skills you learnt in doing so will be able to be applied in new situations.
Life skills need to be learnt too, but we need to put the responsibility for these back on parents so that schools can focus on academic skills.