It's a question of philosophy. In pursuit of the goal of maximum economic output for the society, it is "inefficient" for a parent to be the educator for his/her own children. The way of maximum efficiency should be for children to be reared from birth in large groups by workers at the lowest cost, while the biological progenitors take their highest-value role as producers. This is the Marxist model.
If the goal is to produce an 18- to 20-year-old person with such-and-such knowledge and skills, then institutional schooling also has the potential to be more "efficient," because those providing the schooling can be specialists who convey their knowledge to larger groups. This also allows the biological progenitors of the students to maximize their economic value as producers, since they are freed from the daily supervision of their offspring.
The view of the family in which the very fact of living and learning together at any age is in itself a value is very different from either of the previous philosophies.
Like Marxism, the theory fails in reality.
* The high level of expertise simply is not needed to teach most classes.
* Institutional teachers are rarely as motivated to care for a child as their parent is
* When a child gets to the level where expert teachers make a difference, the homeschooling model allows the flexibility to pursue those experts where the institutional model is rigid and uses a one-size fits all approach.
One of my daughters was very attached to her mother. In a public school, that was a problem because in a room of 30 students, the teacher cannot give every student that kind of attention. The advice given by another homeschool mom was that it was a fantastic opportunity. Let the kid sit on your knee as long as she does educational activities. She will outgrow wanting to be right next to mom, but the education would benefit her an entire life time. It was great advice, and worked just as described.
Oh, my. Learning together as a family is great and even greater through the division of labor.