The socialization quality argument doesn't hold water. The social pressures of public school can be a challenge but they play a vital role in children's development. Gary Prior (a psychologist) said homeschooling is "not real life... When you enter the adult world and are on your own... you're going to have to cope with all sorts of people and situations that may or may not be to your liking." If children aren't exposed to real-world challenges they won't be able to cope in the adult world where they must interact with all of the former children they avoided when they were young.
While people who do not share the "same values" as a child may be more difficult to deal with for the youngster, they may be just what the student needs. Parents might feel that they are protecting their children from harmful viewpoints when they homeschool, but, by keeping them isolated, they are denying them exposure to new ideas that could be beneficial to them. Children shouldn't be kept in cocoons. They need access to experiences that may test their comfort level. Homeschooling simply does not provide this kind of exposure so it can be greatly detrimental to a child's education.