Homeschooling wont leave much for socialising im afraid. And being bullied is a part of life, and in 1 out of the 10 idiots that bullie you, you might find a friend.
Homeschooling will in my opinion make you more of a social outcast than any bulling could ever do. 
However, I agreed on what you say about schools being a day care center for older children.
There are plenty of ways for homeschooled children to socialize. Boy Scouts and Girl Scouts are two of the well organized ones. There’s also sports (as almost all sports for kids younger than High School age happen independent of public schools anyhow).
Though there are some things I think should change anyhow. I think the public school system should really embrace homeschooling, and provide services… seeing as how the parents aren’t getting paid thousands/year to educate their own kids. Simply a good system (especially in higher grades, like middle and high school) that would let homeschool children take a few classes every now and then at the school, whatever a parent thinks they don’t have the skills to teach… maybe they’ve got the core down, but they want their kids to be able to choose some of the electives the parents aren’t knowledgable about. Also, allow them to participate in activities, like sports, band, and JROTC, and attend functions like Homecomings and Proms. Of course, if a good voucher system were in place which compensated home schooling parents as well, they’d need to give up a portion of their voucher (which would go to the school) to participate.
Imp
These previous listings can be learned anywhere, school or no, public or private or what-have-you.