By definition, homeschooling is simply the act of teaching children at home rather than at school. The teaching is most often carried out by a parent, but sometimes also by a tutor.
Historically in Unites States of America, educating a child at home was the status quo. The founding fathers were educated at home, and this was the norm for children. But in the 1800’s, a movement to create universal compulsory education gradually changed the education norm from homeschool to public school. Not everyone has been pleased with the performance of the public school system for various reasons, and in the 1960’s and 1970’s, a counter-revolution arose to return the right to educate children at home to families.
Origins of homeschooling - Raymond Moore and John
The homeschooling movement began in the 1960’s and 1970’s as a response to the increasingly secular, hostile and restrictive environment of public schools. In 1969 Raymond Moore, a former U.S. Department of Education employee and his wife, Dorothy, a former teacher, began to be concerned that entering children into school at too young an age is detrimental to their development. Influenced by the early child development movement in psychology, they believed that a child’s nervous system is just quite simply not developed enough to handle the strains and restraints of the school system. They felt that schooling should be delayed until 8, 10 or possibly even 12 years of age. His Christian-based books earned him a following among Christian family.
Simultaneously, fifth grade teacher John Holt began advocating for returning the control over a child’s education back to the family nucleus in the 1960’s and 1970’s. He felt that school environments were lacking in humanity. Holt was also deeply opposed to the nature of compulsory education in general, feeling that it imposed on a person’s civil liberties. His “learning by living” approach to education is now known as “unschooling”. His books about alternative education earned him a large following from the counter-culture crowd.
Moore’s Christian point of view and Holt’s laissez-faire point of view combined to attract both ends of the political and social spectrum of society. Eventually, the grass-roots movement of homeschooling took off, and turned homeschool advocates into a viable political force in the 1980’s and 90’s. 
Legal resistance to compulsory education
On the legal front, the 1970’s saw the first court challenge mounted against compulsory education, bringing the legal argument against it to the forefront. A 1972 landmark case in Wisconsin, (Wisconsin v. Yoder), determined that Amish people had a right to be exempt from compulsory education laws, as they believed that their religious beliefs were best preserved at home.  As there is no mention of education in the Constitution, homeschooling is still very much a state issue and laws vary greatly between state
Critics Of Homeschooling
The most common criticism against homeschooling involves religion. Because early religious trends gave rise to many stereotypes about homeschoolers, this holds true today, perhaps stronger than ever. Many people would love to see homeschooling outlawed and banned. In Germany, for example it is illegal to homeschool and a family recently had a swat team beat down their door and strip away their kids by social workers all because they chose to homeschool their children. It is unbelievable, but completely true. Is this the kind of society we want here at home where parents are under threat of arrest and children are forcibly removed and given to the state just for homescholing? There is nothing tolerant or "progressive" about this kind of societal oppression. It is frightening, and we hope Germany reconsiders this draconian law.
Today you will hear the argument from staunch critics of homeschooling that homeschoolers are fanatics. The critic will label the parents as religious fundamentalists who want to brainwash their children. This argument states, in summary, "We as a society cannot allow homeschooling because its wrong to allow parents to brainwash their children with dogma, the poor children willl grow up warped and they deserve better than that, so we must compel parents to put them in public schools instead. The public school system will be a great counter to parents who wish to indoctrinate their children." Aside from the anti-religious position in this argument, this idea postulates, somehow that the critic cares deeply for the children even more than the parents, and knows whats best. The critic has made themselves intellectually superior to the parent by declaring, with authority "secularism is better than religion, and children are better off without it.". The critic doesn't care if the children perform well on math, history, and science. They still want it banned simply due to an intolerance against religion. The truth is that if a child is educated at home, and meets or exceeds educational standards, then it doesn't matter what the faith of the parent is, or the faith of a child. If a Muslim child, for example, scores high on a biology test and knows more about evolution than his peers, what right does the critic have to say that the child is not adequately educated simply because the child may believe in Allah as well? This is just religious intolerance at its core, and it is not representative of an open, tolerant, and free society. Freedom of religion is fundamental, and should never be infringed upon. All that should matter, as far as the state is concerned, is whether or not the child meets or exceeds standards for education. Their religious beliefs are irrelevant. The second fallacy of this argument is the assumption that public schools are superior. The public school system has vast flaws. Some districts are highly successful, and some are failing terribly.
According to a 1999, National Center for Education Statistics (NCES) survey, 48.9 % of parents surveyed said they chose to homeschool to give their child a better education, followed by 38.4 % of parents who homeschool for religious reasons. The remainder disclosed that they homeschool for a variety of educational and moral reasons. Only 8.2 % of parents claim to homeschool because they have children with special needs.
The option to homeschool more often than not has nothing to do with religion, this argument is simply not true as the statistics cite. And even when it is true, we run into dangerous ground when we as a society allow beurocrats to censor religion as if somehow it is "bad" for children. When someone looks at Jewish home, for example, and thinks to themselves "that poor child, being raised by religious parents is being brainwashed by religion, we must spare that child from religon and deprogram them in the public schools!". Who is the extremist here? The religious parents, or the person who wants to reach into the home of another family, and force their children into public schools simply because of anti-religious intolerance? Our society, if we are truly a free society, must allow parents the freedom to raise their children the way they want, whether that is under a religious household, or a secular household. The argument against homeschooling due to anti-religious intolerance is not a good reason to regulate the choice of parents, because it strips freedom from parents and gives dangerous power to the government that it should not have.
In summary, most often, parents choose to homeschool because they feel the pulic school system is failing their children or lacks challenging enough curriculum, among other reasons. Homeschooling has everything to do with what a parent feels is in the best interest of their own child. And who is more qualified to know what is best for your child- a parent, or a politician?
Who is being homeschooled?
In contrast to the idea that only the wealthy people are keeping their children out of public schools, most homeschooled children come from modest homes. Although the vast a majority of homeschooled children are white, all members of society are represented in the homeschooling numbers. The typical homeschooled child comes from a two-parent family, and have only one of two parents in the labor force. In 2003, 77 percent of homeschooled children were white, 9 percent were black and 5 percent were Hispanic. Both boys and girls were equally represented in the homeschooling population. Compared to privately schooled children, children in both public school and homeschool are more likely to come from families earning less than $25,000 annually. Homeschooled children are also less likely than privately schooled children to have parents with a higher educational degree, but this number is still greater than children enrolled in the public school system. 25 percent of homeschooled children and 34 percent of publicly schooled children have parents whose highest completed education is a high school diploma or less. 
[“Homeschooling: Back to the Future” by Isabel Lyman http://www.cato.org/pubs/pas/pa-294.html]
[[“Testing the Boundaries of Parental Authority Over Education: The Case of Homeschooling”
Stephen Macedo and Yael Tamir, eds. 2002. http://www.hazpolitica.org/pdfs/homeschooling2002.pdf]
 [“The Characteristics of Homeschooled and Nonhomeschooled Students”. 2003 http://nces.ed.gov/pubs2006/homeschool/characteristics.asp]