Public schools, they claim, are not educating our children, and are a cauldron of violence and immorality. There are indeed problems with public schools. However, study after study has shown that the American public school system is among the finest in the industrial world. It is a very big system, and is statistically, according to the FBI, one of the safest places a child can be. As to immorality, many social conservatives think that the development of intellectual skills and independent thinking among the young, much needed for survival in our modern world, rather than the straightforward implantation of a strict obedience to civil or religious authority, is immoral.
School vouchers have a certain appeal, which has little to do with improving a child's education.
A voucher system is a means to give public money to religious organizations. It is also a means to undermine a teacher's right to organize into a bargaining unit. They don't attack public sector unions directly, but imply that the non-union private sector is somehow more efficient. That is, of course, nonsense. Non-union workers are underpaid and don't usually stick around long enough to pick up the expertise to be efficient.