There is one difference between home schooling and regular school which I'm not sure has been addressed; I've not read every post in the entire thread.
When you have more than one student involved in a learning situation, you have more than one brain and more than one perspective. Hearing and understanding what others think and how others perceive things, having dialogue with others on any issue, etc., is also part of the learning process. In a situation where you have only one student and a teacher/parent, your dialogue is very limited. In the classroom, students have an immeasurable amount of intellectual interaction with others; this enriches the learning process no end. IMO this is a hugely important issue and suggests to me that the multiple student classroom is far more appropriate for leaning than a single parent/teacher learning environment. One of the most significant ways of developing the mind and acquiring knowledge is collaborative learning, i.e., group work. You don't get that at home with just mom. As well, one of the best ways of learning is teaching, and in group work situations, the stronger students tend to become 'teachers,' which deepens their own understanding of what they are studying. Weaker students become more involved in their learning instead of being passive learners. It's a win, win, win situation which you don't, as I said, get in a one to one learning situation.
You would be correct.....If it was 1994 instead of 2014.
See there's something now called "the internet:" This allows interaction with others on a scale you may not be able to conceive.
Go to your library. They probably have a book about the "World Wide Web" that will explain the subject better.
Non-human to human interaction though technology is not in any sense the same as direct in person human to human interaction. I am amazed that any thinking individual would believe such a thing: to me, it is obvious that interacting with someone over the phone or internet is absolutely not the same as interacting in person. Just watch a group of people interacting together, in person, discussing an issue or solving problem, then watch the same with an internet group. With an internet group, you can see there are all kinds of lapses and pauses, uncountable 'misses' in communication, etc. As well, studies have made it clear that body language is the largest element in human communication.
The program I work within has regular workshops to keep us up to date and learn new material. A few years ago, all of these workshops were in person, and we had to travel to site for the workshop. Nowadays, there are internet workshops which are cheaper because there is no travel cost, no hotel cost and the payment for the workshop leader is less. However, these internet workshops do not compare with the in-person one. Every colleague I have spoken to on the matter says the same thing: they much prefer and learn a lot more during the in-person workshop with a group of people and an instructor.
As well, where is the home schooled child to get groups to do a lot of internet lessons with? It doesn't happen now, and is not likely to happen. So your position is extremely weak. In-person group learning far more effective than interacting with someone over the internet. Arranging over the internet group (collaborative) learning is not being done as a part of home schooling and is impractical to contemplate as something that will be done.