From The Wealth of Nations:
After the public institutions and public works necessary for the defence of the society, and for the administration of justice, both of which have already been mentioned, the other works and institutions of this kind are chiefly for facilitating the commerce of the society, and those for promoting the instruction of the people. The institutions for instruction are of two kinds: those for the education of the youth, and those for the instruction of people of all ages. The consideration of the manner in which the expense of those different sorts of public works and institutions may be most properly defrayed will divide this third part of the present chapter into three different articles.
But though the common people cannot, in any civilized society, be so well instructed as people of some rank and fortune; the most essential parts of education, however, to read, write, and account, can be acquired at so early a period of life, that the greater part, even of those who are to be bred to the lowest occupations, have time to acquire them before they can be employed in those occupations. For a very small expense, the public can facilitate, can encourage and can even impose upon almost the whole body of the people, the necessity of acquiring those most essential parts of education.
The public can impose upon almost the whole body of the people the necessity of acquiring the most essential parts of education, by obliging every man to undergo an examination or probation in them, before he can obtain the freedom in any corporation, or be allowed to set up any trade, either in a village or town corporate."
However I agree with Milton Freedman on the issues surrounding public schools. The fact they are accountable to no one is a huge problem that never gets addressed.
Now if you wish to call me a Marxist so be it. However you better start calling some of the Conservative members of SCOTUS Marxists as well because some of their rulings such as Scalia's opinion on VERNONIA SCHOOL DIST. v. ACTON and the opinion that REHNQUIST joined in NEW JERSEY v. T.L.O not only validate their existence but validates their authority of "in loco parentis" (to act with parental authority in place of the parent). I don't agree with such rulings
Don't be ridiculous, Smith predates Marx by over 70 years. Thomas Jefferson and Abraham Lincoln were also in favor of public education, but that doesn't make them Marxists either. It wasn't until the 20th century when public education had become widespread that it was discovered to be untenable for actual education and solely a tool for indoctrination. Once again, read Bukharin. Anyone who supports government-run schools, especially forced government schooling, is a Marxist on that topic, since the only purpose for government schools is to indoctrinate children and young adults into socialism. And yes, that includes Rhenquist and Scalia on that topic.
One cannot favor public education as a reality and still support home schooling. By its very nature, public education must be forced and ubiquitous. Government-run schools and home schools are mutually exclusive. However, since so many people still believe the dichotomy can exist, the purveyors of government indoctrination employ the subtle agit-prop that home-schooled children can be and sometimes are less educated and less "socialized" than their government indoctrinated peers. People who wish to continue to support the impossible dichotomy pick this propaganda up and mindlessly repeat it.
There is no objective, empirical evidence proving that home schooled children are any less educated or any more poorly socially adapted. Indeed, there is ample evidence to show that across three standard deviations, home schooled children are better educated for their ages and as a whole and are better behaved in social settings. Your wife's anecdotes do not constitute evidence of anything other than simple bias.