No one can teach you, you are your only real teacher. People can model, explain, but learning comes from within.
I plan on always homeschooling. I'm not super at math, but I don't need to be. While making my cake, I asked my daughter to help me double a fraction. She easily did it -twice. She sees numbers. My son seems to be following suit. I figure my job is to provide them with the right resources. Right now they are building with k'nex. We do math in the kitchen,in the car, etc. But never on paper or at a table. There is no need. Math is everywhere, so we live it.
Most "subjects" are everywhere, so we just kind of learn about the world as we live. I don't see why this will change at any point. As they get older, and the topics more advanced, we have the internet or neighbors and family members that can be resources for any questions they may have. I also have a really bad book buying habit. My kids have books on everything from gravity to the number zero. We read, they read. What more do you need? If the book doesn't have the answer, google does, and my kids have their own touch screen computers.
I question the whole model of teacher-learner. Real teachers, like Socrates, are models. They inspire curiosity in others, but they can't "teach." You can show others whatever you want them to learn, but unless they want to learn, learning won't happen.
Really, my job is to preserve and encourage their natural curiosity. My oldest reads at a 4th grade level and I never "taught" her anything. She just does it. We have books everywhere -literally, I can't walk around my house without there being books on the floor! All of them love books, and my 15 month old can find the letter S in her ABC puzzle -her name starts with S. She loves the puzzle, and I showed it to her one day, and that was that. It meant something to her, so she learned it.
My plan when they are older is to just send them to the community college for advanced math. Why take it twice? If they are mature enough, interested enough, and capable, the community college will be our Highschool alternative.
But mostly, we are involved in a coop, and I'm sure my kids will just be at a free school when they are older. I doubt the school will have teachers outside of the parents, but if we pool our resources, everything should be covered.