Fostering Competition

A Republican friend of mine was complaining that there should be a voucher system or some other way to fund private schools as a way to "Foster Competition" with the public schools as a way to improve them.  Should we call this the "Private Option"?

I told him that if you replace the word "school" with "health care" and change "private option" to "public option" you have the exact reason why we need a public option in his own words.