Look, I went to public school and I am well aware of its shortcomings, so don't condescend to me. But your purported solution would be worse than the status quo, and that's an accomplishment.

Home schooling is not a replacement for public education, and a basic income social program is not a replacement for directed government spending. I can't even begin to list the overwhelming problems that would rapidly develop in such a system: inequality of access to education, loss of standardization heading into higher education, expansion of free ridership, inflation of basic costs...

If I believe a thing to be true, wouldn't not sharing that with my children be abuse?

No. We believe that freedom of thought and belief is a fundamental human right. Beliefs are a matter for the individual, like, say, sexual preference. Regardless of what you believe, it's not your place to tell anyone else what they should, but especially someone who isn't old enough to make their own decision.

Children need guidance from somewhere, where better than their parents? You think the rest of the world would do a better job? Nothing will stop a child from changing his or her mind when they get older, but they need indoctrination of some sort in order to reach a basic level of interaction with society. Critical thought, judgement and self-determination are part of parents' indoctrination of their children, but so are basic morals and values -- often these are represented and transferred as religious beliefs. The fact that this indoctrination happens through a framework of religion does not make it harmful.