Homeschooling in the Westover household is based on religion. To be more precise, it's based on the variant of Mormon fundamentalism practiced by her parents. Above all, this means that Tara and her siblings are being prepared for the Last Days, the apocalypse that will dramatically bring an end to the world, and which Tara's parents believe is imminent.
As a crazed conspiracy theorist as well as religious fundamentalist, Tara's father believes that public schools are part of a secret government plot to brainwash children into accepting its agenda. That's the primary reason why he keeps his own kids at home, but instead of offering them a rounded curriculum by way of an alternative, he subjects his children to a daily diet of Biblical literalism and conspiracy theories.
Tara's parents appear hostile to the very notion of education as most people would understand it. They make no effort to teach their children basic math or grammar. As fundamentalist Christians they're profoundly hostile to modern science, and as for the humanities such as English Literature, those are thrown out because they're part of the godless culture from which the Westovers wish to escape.
In one particularly striking episode in the book, Tara, who's finally attending school for the first time in her life, raises her hand in class and asks what the Holocaust is. This gives you some idea of the total ignorance in which the Westovers kept their children for so many years.