This makes us all richer in the long run, and is not the zero sum game you claim it to be.
When the government is the monopoly supplier of a good, it's difficult to visualize the world being any other way. But there are instructive test cases: just look at how much more vibrant religious life is in the absence of a state religion. (I'm a Pastafarian, BTW. ;-) Or look at how much scarcer and less varied food is in command economies.
Education is tremendously valuable, and there are powerful incentives to unlock that value. I think you'd be surprised at the institutions that would arise to help you become a competitive worker in the absence of a government monopoly on education.
Maybe if Patri's Seasteading Institute (http://seasteading.org/) takes off, we'll get to find out. :-)
Yes there are. Look at all the countries at the top of the list on education. They all have strong federal education. No country with a purely private education system is even on the list!
That's because no such country exists. But no country had freedom of religion (in the modern sense) until 1787, the year the U.S. Constitution was ratified. That doesn't mean it was a bad idea.
So there was no country in the world prior to 1787 that ever allowed it's citizens to practice the religion of their choice? Are you sure about that?
edit: you do realize that the US primarily had private schools in the early days. The idea that no one ever tried private education is simply false. So is the idea that America is the first country that ever allowed it's citizens to practice the religion of their choice.
Transfer payments aren't the same thing as a centrally directed allocation of goods. You can still choose where to spend them. Even targeted assistance for education still lets you choose what institution to attend.
The transfer payments in the current system pay huge dividends over market allocation of educational goods, because the market tends to give these goods only to the children of those who are already well-off.
However, the primary and secondary public school system is radically broken, mostly through the fault of the government. It needs not only more competition, but also the elimination of local funding through property taxes.
Sum up the total cost of increased prices due to taxation and your personal lifetime tax burden and it's not nearly as clear-cut that you come out ahead with public schools. Add to that the distorting effect of school monopolies on incentives and quality (virtually all public school teachers are in the bottom half academically, etc.) and you've got a shaky argument for government education, even for your case. I'd bet that even you would have been better off if schools were provided on the market.