That's not correct. The school voucher would allow the parents to get a subsidy equivalent to the amount of the taxes THEY pay that would go to the public school to use for tuition at any school. People aren't asking for anyone else's money just what they provide so it can be used at a school of their choice even a private school.
No. If the voucher was only the amount the parent pays in property taxes it would not be enough to pay for private school. It is usually the amount spent per student in that district which is much more than the parent's actual taxes. They average $2,000-5,000 but there are as many variations as states using them. Vouchers do not exempt the parent from still paying taxes. The money goes directly from the government to the private school.
Some are tax credits and others are primarily for low-income families in "failing" schools. Some are for special needs kids because many schools cannot afford programs with all the special needs mandates.
So far, so good. The real problem is that these schools are exempted from many of the state school regulations. This means they may have no standards or financial accountability and non-certified teachers. Many of the charter schools have already closed down after spending money on private homes and high salaries. Some states do require some level of certification and standards but some complain that is interference in raising their child.
https://www.greatschools.org/gk/articles/school-vouchers/