Who Should Get Private Schooling?

I often wonder who deserves the best schools. Is it the rich families, living within private gates of their community, that should send their children to the best private schools? Sure, they can afford it and they want to do what is best for their kids. But that brings me to the child living in the slums of a city...they may attend the worst school in the area. Is it the child's fault his/her parents cannot afford a better school or a better neighborhood? Will this child end up the same...living in the slums, barely making ends meet? Wouldn't it make simple sense to allow these children to attend different schools, where they can learn, prosper, and hopefully get out of their current situation? In my simple mind, if this were to happen, all the schools would be driven, if not forced, to improve. Does our country not want every child to succeed?
School choice would stimulate change within our many failing districts, and finally allow children to reach their potential. The American Federation of Teachers strongly opposes school choice, and many other education reform tools. Unions were strong supporters of President Elect Obama, who is also against school choice. Now, they are all in a tricky spot. The Obamas' will most likely send their two girls to one of several elite private schools in DC; and why shouldn't they? They can afford it and want the best for their children.
Now, the AFT says that is okay. Anyone else find a problem a strong school choice opponent using private schools when he promotes public schools and refuses children from choosing other schools? I am in no way saying the Obamas' should choose a failing DC school; I am only suggesting if they feel the schools are not good enough for their girls, why are they good enough for any child? Why does the AFT feel it is okay for the president to not choose a public school when he feels every other child should?
CNS News reports on this in Okay for Obamas' to Send Their Kids to Private Schools, Teachers’ Union President Says
President-elect Barack Obama and his wife Michelle “have every right” to send their children to public or private school, and no one should “criticize” their decision, Randi Weingarten, president of the American Federation of Teachers (AFT), said in an interview with CNSNews.com on Monday at the National Press Club.