We homeschool for a number of reasons. One is worldview. We don't like that a lot of public schools teach a lot more than math, reading, and writing, things that parents should be able to teach their kids, especially in those early formative years when kids aren't yet secure enough to ask questions or debate back. Another is educational quality. Most of the schools that we're familiar with or that are in our area spend so much time teaching those non-academic things and teaching to the lowest common denominator that the education is really lacking. We're also military and move a lot, so teaching our kids ourselves will make sure that their education is more consistent and that they don't miss anything major or study the same thing twice in a row because of switching school districts.
As for socialization, maybe I'm weird in this way, but personally, I don't *want* my kids socialized by twenty other kids their age who are just learning manners and politeness and how to treat other people and aren't that experienced in it themselves. I would much rather my kids experience the majority of their socialization from their parents, grandparents,and other trusted adults and cousins/older friends, who have enough life experience to provide good examples of behavior. They'll have plenty of chances to practice their budding social skills on other kids during church, activities, homeschool groups, and the like, but I don't want the majority of their lives to be spent with twenty other kids exactly their age.
We plan to homeschool our kids the whole way through, but we're open to looking at alternatives if it turns out that some of our kids need a different experience. In that case, though, we'll probably go with a private or charter school rather than a government school. We'd also like our kids to take some community college classes when they're high school age, so they can get some practical classroom experience, working to deadlines set by other people, and being responsible for their own class, to help prepare them for the real world or college.
As for homeschooling being legal, as others have said, it's legal in the UK, but there are some countries where it isn't legal at all (I believe the Netherlands and Germany are two examples, although I'm not absolutely certain about those).