"False Argument?"...Vs what?
Your arguement? The one filled with qualifying "if you" that begins every thought?
How about this: If I give it even a moment's thought, then I realise you're ignorant.
THEORETICALLY, vouchers can be used to send your child to any school.
But EVERY school is not available to EVERY parent.
Therefore, in REALITY, parents can only choose schools that:
A. provide transportation for their kid, or
B. Are on the way to work in the morning AND keeps the kid until they get picked up after the parents work, or
C. One parent doesn't work, but spends the morings and afternoons transporting kids, and the rest of the day eating bon-bons and watching soaps.
Which of these works best for the AVERAGE AMERICAN FAMILY?
A. Most Americans send their kids to school on a bus.
So, the voucher system would resolve nothing: Regardless of which schools were best, MOST parents will continue to send kids to whichever school they can be most easily transported.
Vouchers will work great for the very few parents in categories "B" (rural) and "C" (suburbian soccer moms).