the children being homeschooled are limited to their parent's ability to relay information and the previous schooling of the parents. In a school setting, children are provided with perspectives and knowledge from a very wide pool of minds.
This is not true. Homeschoolers have a wide array of resources at their disposal. Not only can the parents relay information to their children but they can take advantage of distance learning courses, co-ops where parents share their knowledge of particular subjects, also many homeschoolers are enrolled in classes just for homeschoolers offered through local museums and often older homeschoolers are enrolled in college classes for dual credit. Homeschoolers are unlimited in their ability to seek knowledge in a wide variety of places. Also many homeschoolers are able to travel and experience different cultures with their families due to the flexibility homeschooling offers.
Socially, homeschool does not expose children to peer pressure. Peer pressure can be a good thing and it can be a negative thing. Regardless, children need to learn how to handle peer pressure situations and how to interact with their peers (especially the ones that are different from themselves).
bias of the parents (whether for or against religion) will color the type and method of education. Even atheist children need to learn how to talk with and interact with religious people.
Finally, I find the motive of parents who show a desire to homeschool their children to be selfish. They want to have 100% control of what is let into their child's brain.
Homeschooling is a valid educational choice and a truly liberated mind would embrace homeschooling and the freedom it offers.