In the 1970s Raymond S. and Dorothy N. Moore conducted four federally funded analyses of more than 8,000 early childhood studies, from which they published their original findings in Better Late Than Early, which concluded that, "where possible, children should be withheld from formal schooling until at least ages eight to ten."

According to the Moores their analysis suggested that children need
"more free exploration with... parents, and fewer limits of classroom and books," and
"more old fashioned chores – children working with parents – and less attention to rivalry sports and amusements."

However they only advocated a later start to formal schooling which they felt "encourages peer dependence"

In contrast Rob Reich wrote in The Civic Perils of Homeschooling (2002) that homeschooling can potentially give students a one-sided point of view, as their parents may, even unwittingly, block or diminish all points of view but their own in teaching.
He also argues that homeschooling, by reducing students' contact with peers, reduces their sense of civic engagement with their community.

As many children in America are educated at home for religious reasons (the last census stated over a third) other arguments against have included -

Lack of socialization with peers of different ethnic and religious backgrounds;

The potential for development of religious or social extremism;

Children sheltered from mainstream society, or denied opportunities that are their right, such as social development;

Potential for development of parallel societies that do not fit into standards of citizenship and the community. (as demonstrated in some of the more isolated 'cults')

Of course registration and effective monitoring, as carried out in other European counties where home schooling is legal,* should be able to recognize where education becomes 'indoctrination' in race hatred for example.

*Homeschooling is illegal in Germany (with rare exceptions).
'Generally Illegal' in Spain, the Netherlands and Sweden.