1) I'm responsible for the raising and education of my children, and I'm not going to outsource the bulk of that to strangers.
2) Less time-consuming. From talking to my friends who have 2+ children in school it sounds like they spend about 1 hour per day on average driving their kids around to and from school (not counting extra-curricular activities, parent teacher conferences, homework help, etc...). My mom says her steady-state time expenditure was around 40 minutes per day for all 3 of us, mostly grading math and papers.
3) Way better outcomes. Homeschoolers average at the 87th percentile in national standardized testing, and homeschoolers whose parents make less than $35K still average in the 85th percentile. (http://www.topmastersineducation.com/homeschooled/) On the anecdotal level, I'm a former USAF pilot-turned drone guy, my brother is a successful artist, and my little sister is working on her PhD in Aerospace Engineering when she's not kicking all our asses at fantasy football.
4) Better socialization. Yeah, I said better. I admit that I'm less used to spending time with people my exact age than most of my peers, but I interact much better than they do with people younger than me and people older than me. Funny thing, it turns out once you're out of college, most of the rest of your life will be spent with people who aren't your exact age. Homeschooling prepares you for that way better than public schooling.
5) "The Underground History of American Education", by John Taylor Gatto. Just read it. It'll blow your mind, and it's well-supported. TL;DR, our school system was modeled on the Prussian system designed to build an army that could beat Napoleon's troops. It's designed to create obedient myrmidons who don't know how ignorant they truly are. Don't worry, I'm sure your school was different.