Teachers are Agents of the Father
Your children should understand delegated authority. If you homeschool, you might have to be more intentional about teaching them this concept.
They should always obey their teachers. But you should help them understand why they need to obey their teachers, and for this case, “because I said so” is actually a legitimate reason.
In fact, it is the reason.
As the father, you are responsible for your children’s education. As you attempt to manage this responsibility, you may decide to delegate part of it to others. Teachers would fall under this umbrella. And yes, this also means public school teachers.
Their authority derives from your authority. Despite what the teacher’s union or local school board may insinuate, teaching your children is your business, and teachers are not free agents. They are agents of the father.
And that is why your children should obey their teachers. You have ordained their teachers with some of your authority, and so they should listen to their teachers as if they were listening to the words of their father.
There are exceptions, of course. Delegated authority is never perfect. The stream gets thin in one place, it rushes with rapids in another, and somewhere a family of beavers has built a dam. Fathers and teachers are human. Flawed.
Delegated authority is also limited. A teacher tasked with teaching a child English grammar should not take it upon themselves to teach them how to shoot a gun.
But the default assumption should be one of deference and obedience.
After all, your own authority as a father is delegated as well. It is not innate but flows from the Father. Delegated authority is built into the foundation of the world. Therefore, to navigate the world properly, your children should understand the concept.
This means that to be a responsible father, you and their mother cannot be their only teachers. Some options, if you homeschool:
Music lessons (piano, guitar, etc.)
Bible class at church
Co-ops where other parents teach certain subjects