Education under an anarchist society

I would describe myself pragmatically a minarchist however under utopian circumstances I believe an ancap society is the most logical and consistent form of society based off my beliefs.

yes ik most minarchists dont believe in public education i still consider myself one however. I believe the only role of the state in my beliefs would be to protect property rights (military,police,courts) but I also believe in public K-12 schooling.

I do believe the private sector would do a much better job at educating our children however my main reason for public schooling is I believe education is critical for a society and everyone should atleast have basic education to function. My issue with an ancap society to put simply is how would the impoverished afford to send a kid let alone multiple through schooling?

I think its dishonest to assume there would be zero poverty under any type of society and I have a hard time believing impoverished families could educate their children through the private sector. We already can see how much private schooling costs and most families cannot afford that (yes i believe the price would go down however i dont think itd be down enough for everyone to afford)

So can anyone change my mind? How would a fully privatized education system be able to educate all throughout society?