Why Homeschool Privately?
As parents, YOU know your children better than any "experts" and with God's help will make the best decisions about which curriculum to use, which subjects to focus on each year etc... Are you fearful about this responsibility? That is why having a support group like CFS Poway can be so helpful. Other parents who have "been there, done that" can help you walk through each stage of your children's education.
Enrolling in a public institution, whether charter or through a regular public school system means you will give up some of your freedom. On a regular basis you will have to prove to the expert teacher that you are doing a good job of instructing your children. Whether overtly stated or not, they consider themselves to be in charge of your child's education and can demand that you turn in x, y, and z documentation if they feel you are not doing enough.
Some reasons I've heard for why homeschooling through a public institution is a good idea:
Financial - "They give us FREE curriculum and money for various extracurricular classes"
Many have found the free secular curriculum given out by the public institutions to be subpar and end up purchasing their own curriculum anyway. While many charter schools tell you it's ok to use Christian curriculum, the law says that if you receive government funding for your education, you may not receive religious instruction during regular hours of instruction.
Yes, they get help paying for art or sports, but ask yourself if you have a true hardship and whether it is worth giving up your freedom.