Competition is not fair if the playing field is not level. Poor neighborhoods often lack department stores, grocery stores, banks and other services. Education is a vital public good, and competition is about wiping out your competitor, not making him better. Simply passing public funds through a family does not alter the fact that public money is subsidizing private and sectarian schools. With tuition tax credits, parents use their own money, not the government's.
Tax credits are public dollars the government has relinquished.
Even though the funds are not cycled through the IRS, the fact remains that tax dollars which would be used for public schools are going to private schools. Private school tuition is not a tax, it is an additional expense some parents have chosen to pay. We all benefit from an educated citizenry and are expected to support certain basic public services whether we use them or not. Watch the use of words. Voucher programs are not grass-roots driven but are often promoted by wealthy foundations with political agendas.