I have not responded to the poll because, with respect, the options tend to be too absolute (such as thinking homeschooling is dumb). Home schooling is not popular in either the UK or Australia, but I have met one person who was home schooled, and while 'a single swallow does not a summer make', he was not a good advertisement for the system. I will qualify this by pointing out that he was part of a fundamentalist religious sect, so I doubt he was representative of the breed.
I have two problems with coming to any definitive view on homeschooling. The first being that I went to Public School (note the capitalisation - it means something different in the UK from what it means in the USA). The teachers were very highly qualified (few did not hold a doctorate in the discipline they taught) and by and large, both proficient and unbiased. (My school has the highest academic record in the UK - and has had for a couple of hundred years.) I was not therefore aware of the 'political agenda' - liberal or otherwise - of the education system to which I was subjected. I was aware of having available to me a master in whatever discipline I was studying, and to whom I could refer (outside class) with any issues therein which troubled me.
The second problem flows on from the first, inasmuch as I consider the cumulative effect of so many highly qualified teachers in all disciples to be difficult to replicate in the average well-educated household consisting of two adults, whose economic responsibilities might preclude them spending all day educating their children (assuming they are adequately qualified to do so right up to university entrance level).
I can see why the religiously fundamental might want to shield their children from what they see as overly secular influences, but I can also see why the German state has made public education mandatory. It is my view that parents should not have sole responsibility (and carte blanche) as to how their children are informed about the world in which they must live. A very wise man once wrote - "Your children come through you, not from you ..." We are not the property of our parents to indoctrinate as they wish.