Parents should be able to send their children to the school of their choice, and they do; but the public should not be expected to pay for their private choices.
The public has a civic obligation to support public education. Even if you don't have children, you pay taxes to educate the children of the community. Even if your children are grown, you pay school taxes. Even if you send your children to private school, you pay school taxes. Public schools are a public responsibility.
If you don't like the public schools, you are free to choose a private school, a charter school, a religious school, or home school. That's your choice. But you must pay for it yourself.
We all pay for police and firefighters. If you want a private security guard, pay for it yourself. We all pay for public schools, even if we don't patronize them. They belong to the community. We do so to invest in the future of our society. It is a civic obligation.
We all pay to support public libraries. If you never use the local library, you still have to pay the taxes to support it. If you prefer to buy books instead of using the free public library, don't ask taxpayers to subsidize your private choice. Buy your own books. Pay for it yourself.
The taxes you pay support the common good, not your private preferences. They pay for highways you may never drive on, fire departments you may never call on, beaches open to all that you may never set foot on, public parks, and a range of services and facilities open to all without fee.
When it comes to education, there is a simple rule: public money for free, democratically controlled schools, private money for private, privately-controlled, and religious schools.