I don't have the exact stats in front of me, but the majority of homeschooling in this country still seems to be rooted in some kind of religious/moral orthodoxy that parents use to teach their children their very narrow worldview and that any abberations from that view are heretical/sinful/immoral. This probably doesn't apply to most of the people that read this forum, but I have to state it.
TL:DR- my issues with homeschooling are emotional development, socialization, and subject matter expertise. Please clarify/confirm my thoughts, as they are not meant to be inflammatory.
Background: I'm not a homeschooler but I hope to start when my daughter reaches pre-k age later this year. I've been doing a ton of research on the topic to make sure it's a good fit for my family. I'm also in a graduate program working toward teacher certification (which sadly only makes me want to homeschool more because of what I've seen in public schools.)
Your assertion about why people choose to homeschool: according to data from the National Center for Education Statistics, during the 2011-2012 school year, religious reasons were fourth in the list of reasons families homeschool. The majority of families (25%) said they homeschool because of concern about environment (meaning safety, drugs or negative peer pressure), while 21% cited other reasons (listed as time, finances travel and distance). The third highest category was dissatisfaction with academic instruction, which was the reason for 19% of families. Interestingly only 16% of families homeschool for the desire to provide religious instruction, and 5% to provide moral instruction.
Another part of your post I wanted to touch on was subject matter expertise. I don't think most homeschool parents operate under the assumption that one (or both) parents will be the sole source of knowledge for their student. There are co-ops that meet to receive whole group instruction in some subjects. There are tutors, online classes, and local resources (colleges, enthusiasts) and I think many homeschool families rely heavily upon outside resources for the tricky subjects once you get beyond the basics.
As far as the emotional development, I see kids every day in the public school setting who think they are speshul sneauxflakes and think the world revolves around them. That's more of a parenting issue and not an issue of what educational setting they find themselves in.
Lastly, the socialization issue is so played out and over discussed. Since you're an adult, have you recently been forced to socialize with other adults the exact same age as you? It's just so weird to me that people's definition of socialization is the school setting, in which we cram 30 eight year olds into a room and think it makes them socially competent. I'd like to believe that my daughters will get ample socialization through our family friendships, volunteer work, extracurricular activities, and life in general. I don't see how forcing her to be around other 4 year olds will make her more social than allowing her to communicate daily with people ranging in age from 2-99.
Edited to fix missing parenthesis.