I've ummed and ahhd about joining this thread. Here goes, please don't shoot me.
I would prefer my children to go to school (don't have any just yet ) but accept that there may be situations where HE is a better option. DH and I are agreed that if he is posted to the back of beyond when we have primary aged children we would consider HEing with reference to the NC and with support from the CNED so it would be more school at home and we would only do it as a temporary solution at primary age. If the situation arose when they were secondary age they would go to grandparents or board. Similarly if they had SN or were being bullied I would have no qualms about removing them and HEing but it would always be with the goal of retuning to school.
Academically I would be able to teach a rounded curriculum until the age of about 13. I have As at A-level in an art, a humanity and a science with 10 good GCSEs plus a degree with another from the OU in progress which will hopefully be an Open degree and plug gaps in my knowledge from only being able to take 3 A levels because that's what school would allow. We're a bilingual family in 2 mainstream European languages with working knowledge of 2 more. If that wasn't the case I personally couldn't even begin to contemplate HE but I'm relatively confident we could fill the gaps. I wouldn't plan to do it all myself though!
Equally important I would be confident actually teaching because I was a governess until I married DH and that was my job. Different circumstances but enough to reassure me I could do it.
I understand the pitfalls of HE, having been there with someone else's child and think I know how to avoid them. We are very lucky that if DH were to be sent somewhere that local schooling isn't an option I wouldn't be working anyway and his salary would reflect that so we could afford it. So why wouldn't I do it after primary, and even then only reluctantly?
It boils down to the fact that school is the norm and unless there's a very good reason for not going such as illness or there not actually being a suitable one that's what the vast majority of the population do. It's an expectation people have, it's a common experience that you carry throughout your life and I have a weird feeling of kinship with any alumna of my alma mater! School prepares you for exams and for qualifications. It encourages you to compete with your peers and teaches you to be a small fish in a big pond. It would always be the default of option for me. I couldn't do my children justice at secondary level. I hope they will be ambitious and want to be doctors or engineers or archaeologists, I don't really mind what exactly! But I don't know whether I would be enough to get them there alone/with the support of other HEdders. School would provide them with a better education IMO. Schooling and education is really important to both DH and I despite our different experiences. I loved school for the knowledge it gave me but was appalling socially at school - different in extracurricular activites though, which is odd. He loved it for the social experience and schoolwork was a minor inconvenience which could be knocked off quickly (bright, tests well) but didn't merit serious thought. If our children are anything like us school is the best place for them because I would, quite frankly, be inadequate all other things being equal.
I would probably feel totally differently if my child had been severely bullied and it was a matter or rebuilding confidence and rehabilitation, for want of a better word. Or with an SN child whose needs weren't being met. But for a child who just plain didn't like school there are things in life you don't like but have to do. For a child who was 'different' (by which I mean slightly kooky) sometimes you have to bend a little and go with the mainstream so they'd stay in and either deal with being different or learn to adapt at school whilst being allowed to express themselves at home.
I agree there's a negative perception about HE and HEddrs which probably forms part of my reasoning against. Not because I think they're weird, I know they're not all weird from meeting them, and I know they HE for different reasons but some are and that's the image people have. If I could avoid it I wouldn't put the burden of that perception on my children for the rest of their lives.
This is all my personal opinion based on me because I think it's a decision that can only be taken with a knowledge of oneself and ones family.