In homeschooling, you can advance in things you like to do. For example, you enjoy doing history, so you do two lessons a day, and then you finish that grade, and you can move on to other things.
In public school, there’s always that slow student, and you can’t advance because of him/her, and you’ll get bored. If you’re the slow one, usually you’d just fall behind and not able to catch up.
But in homeschooling then you’d be able to watch the lesson again, and actually, learn at your own pace.
Another thing, homeschooling can only take 4-5 hours, and you have the rest of the day free to do other things, like your hobbies or after school activities. Once I finish my schoolwork I play guitar and practice my piano, and I also have swimming after.
As in public school, you spend 7-8 hours a day just in school. Then you have homework after school and won’t have time late at night since you have to go to school early.
In public school, you learn whatever your teacher teaches you. Then you take tests, and if you get a good enough grade, then you don’t need to retake the test, and you forget. In homeschooling, you keep the information and actually learn.
In the system I use, there are 4 days of learning, and taking down notes, and on the fifth day, there’s a review and an essay to do. And I think that’s very effective.
If you’re afraid that you won’t make friends because you don’t go out and socialize. Well, there are programs for homeschoolers, for example, I go to a public speaking club, mostly because I don’t socialize much with kids my age or whatever. And I go to a swimming class/team and I get on with people just fine.
In conclusion, homeschooling is more beneficial, you have more time for other things, and have more freedom. And not just learn but also remember most things, and not what the government wants you to learn.