I'm a huge homeschooling fan, having taught remedial reading & writing to upper grade primary children & decided that a very poor job had been done by the educational establishment. For 11 & 12 yr olds not to be able to decode words like station, fashion caution is appalling ~ & it is rampant in the Qld system!
Homeschooling is not like regular school & does not have the same objectives. Firstly the idea is not to teach anything as such but to teach the child how to learn so that they can teach themselves what they need to know. I will give you 3 examples. YD asked to learn German when she was 6/7 so she could watch a German language show with me without me going nuts translating for her. I do not speak German but I found an American ex~ consulate German translator willing to take her on. Her German accent is still excellent though she is now only using her German for music but having learnt a 2nd language with confidence she takes on all the rest: Latin ,French, Italian, Hungarian... She knows how to go about it. Later we bought her her 1st computer & I worked hard to get it up & running for her. The 1st thing she did was crash it. Unwilling to admit what she'd done she wiped the whole thing & learnt how to reset it herself. Thirdly neither of us like math. Neither of us wanted to do upper math. I wanted the child to be able to budget & that sort of thing so we did no algebra or trig. Recently the child wanted to learn it for a job application & did so.
It's not how good the teacher is. Its not how much the teacher knows or the student learns. There are plenty of college grads who never read another book once they leave college. The trick is generate a love of learning in a student & the ability to learn how to learn. Sadly most schools only teach you how to pass an exam & kill both innovation & the love of learning.

And any homeschooler will tell you their kid socialises with a much wider variety & ages of people than any school child because they are constantly out & about in the community. I brought my older girl home [@ her request] in grade 9 & watched a reticent, unwilling to express an opinion child develop into a wonderful debater in a bible study class made up of a huge variety of ages & races who, unlike her peers, were willing to listen to an alternative viewpoint.
Given the nature of humans I'm sure some homeschooling parents do a lousy job but most I've known are very thorough & do a much better job than our school system ~ including the private system! I know because mine had heaps better general knowledge, particularly in history & Literature [ obviously my strengths] than their peers & when state tested outperformed them.
Descending from
my soapbox now.