tell her you feel like your missing out on your experiences and you feel anti social at home all the time. she might get allittle mad. like start out like "mom. just hear me out." then say "well, i really want to go to real school. i think im missing out on my experiences. i just feel like i need friends i can see everyday. you did a great job but im ready for public school." then if she says no, then tell her "mom i really need a life to live, i dont have any here" then she'll probably say yes if she cares for your feelings, she'll be stressed or mad, but i dont think she'll yell at you. don't say it in a whiny tone or any attitude, that will lead you to n automatic no.
Here are some talking points. - It is not possible for your mom to know everything unless she is a savant. She can only teach you what she knows. - Your mom is not a professional teacher ( I am assuming). A teacher goes to college and is taught how to teach. - Our species - homo sapiens - are very social. This is part or our civilization. School is where you learn to socialize, cooperate and coordinate with other people. An extremely important lesson in modern society. - The best way to develop new ideas is to challenge the ones you have. When you live in a place where everyone thinks the way you do, you will NEVER be challenged to think in new ways. - Last resort. Go on strike. Refuse to study. Insist that you will call the authorities. The law says that your parents have to give you an education, whether at home or through public school. This will cause friction in the family so I would use this only when all avenues have exhausted. Also, don't expect your family to help you with school if you take this route - you will be on your own.