One of the key assumptions of our political system is an "educated electorate" - that is, a populace well enough educated to know what is, and what is not in its own best interests. You pay taxes to make sure that your neighbor's children are educated to ensure that they don't get conned into voting for something that is bad for you, for them, for everyone. Public Education as it is practiced in the United States of America came about in order to make certain that the electorate was indeed educated to this end.
Alas, our public education system has failed. The depressing evidence is all around us.
Therefore, reform is in order.
If you believe that the typical parents have the best interests of their children at heart, and that they are (in the majority) able to determine what courses of study are most likely to lead to success in our society, then it is not much of a leap to allow parents to choose what school their children attend. In part, this happens already - people move to "better" school districts to ensure their children receive a "better" education, if they are able.
However, those who do not have the means to move where they will are stuck with whatever passes for public education in their area. They are, in effect, a captive market for those schools. Their ability to affect what happens in that school is mostly limited to who they can elect to the school board, and if the decision goes against their wishes, they have little recourse.
As a countervaling force, I think a school voucher system is a wonderful idea; allow parents to control to which school the state monies earmarked for the education of their child will go. In this way, the parents can "opt-out" of the public schools when those schools fail them. This puts even those parents who are economically disadvantaged in a position of power.
There are, unfortunately, several different versions of "school vouchers" - it depends on who you ask what this term means. I mean that parents of all school-age children should have the ability to direct the monies allocated by the state for the education of their children to the educational institution of their choice. For me, that means all monies. Schools which do not attract a critical mass of children and their parents will simply fail and be closed. To reduce the incentive to skimp on the education at the schools, a "school" must be a non-profit entity.
The people who practice home schooling would like very much for their educational expenses to be deductible from their taxes, presumably up to the amount the state would spend on their children otherwise. This is a bad idea because the economically disadvantaged do not have the income to spend on education for their children in the first place; better that the home schoolers get the voucher themselves, so that everyone can play on a level field.
It is also my understanding that many home schoolers pool their resources - this is, in effect, a "school" even though it may not be formally recognized as such. It may be worth relaxing the definition of what a "school" is, in order for such cooperatives to qualify for vouchers.
The only serious danger is that a majority of the nation's students will get sent to crazy religious nuts who will train them to be blindly obedient drones, instead of encouraging them to be free thinking, creative individuals - woe betide our society if that happens.
Nonetheless, the existing public educational system is a scandal, and must be deeply reformed. School vouchers are one means to that end.