School vouchers take money away from the public system to give to private and religious schools. It is one thing to get a choice in where to send your kid to school, it's different to ask everyone to pay for that private choice.
That makes no sense.
Let's look at it from first principles. We as a society have decided that it's in everyone's interest to educate children, so much so that we tax everyone to raise money to spend on education. How does giving parents a choice of which school to send their kids to (assuming the schools are of equal -- or better! -- quality) undermine that societal interest, especially if the voucher amount is less than what the public school system would have spent on the same children?
I have a bias here: My oldest son is neuroatypical and was badly failed by the public school system, even after all of the help that my wife and I could provide. I actually spent a good chunk of his second grade year sitting in the back of his classroom working on my laptop (because I had a job where I could do that) so I could be ready to provide the teacher the support she needed to deal with him. She appreciated it, but I couldn't be there all the time, and in the end it just didn't work.
So, we started looking for alternatives. What we found was a small private school founded and run by a couple of parents who'd had a child in a similar situation. Classes were tiny (no more than 8 children per teacher) and it was staffed with experienced teachers who were frustrated with public school bureaucracy. Probably a third of the kids there were like my son, in that they just couldn't fit into the public school system, the rest were kids of two working parents who appreciated the school's other benefits, primarily "latch key time". The school allowed students to be dropped off as early as 7:30 AM and to stay as late as 5:30 PM (though not both) and the school provided supervision and educational entertainment. The cost (in 1998) was $3000 per year, which covered tuition, fees, meals (two hot meals per day, breakfast and lunch, plus afternoon snacks) and school supplies. At the time our state (Utah) spent about $5000 per student per year, but that didn't include meals or supplies.
My son loved the school, and flourished there. He caught back up and surpassed grade level in all subjects and became an avid reader. Interestingly, the school did not believe in assigning homework to grade-school children, all work was done at school. You might think that was educationally limiting, but the school gave all students the same standardized tests as the public schools every year and consistently outperformed the public schools by a large, large margin.
We didn't need the latch-key time (my wife was a stay-at-home mom and my job gave me flexibility), but we let him stay late a couple days per week because he begged us to.
This private school was better than the public schools in every possible way. Cheaper, academically superior, provided better food and more flexibility for parents (though no buses).
In what world would it not be better to expand that sort of option through vouchers? Had the state offered a $2500 voucher (half of what they spent on public school students), it would have make the private school accessible to many more parents, doing a better job of achieving the social goal of educating children. There actually was a voucher law passed by Utah in that time, but it was struck down by the courts.
What actually happened, though not until after my son had spent three years there, third grade through sixth (they didn't do Junior High), was that the US Air Force and the city forced them to relocate because they were just past the end of an active runway and there was concern that a military jet could crash into the school. But they were operating on razor-thin margins and could not afford to relocate without increasing their fees by 30%, which most of their customers couldn't afford. Vouchers, even at 50% of the public school cost, would have made that affordable. So instead, they closed their doors and the area lost an incredible resource.
I'm not, of course, claiming that my son's school was typical of private schools. But does that really matter? If the state can verify that the schools are doing a good job (standardized testing plus occasional inspections should be sufficient), and if parents prefer them for whatever reason, why not? What is bad about offering a choice? What is bad about giving public schools some competition, hopefully forcing them to provide better services and be more efficient?