Should private schools be abolished?

A parent and their child have the right to choose where the child goes to school. Locally, the state shool might be failing, and it is unfair to the child if they have to go to this school just because the state wants to penalise those who have worked for their money and want to spend it on a worthy cause i.e. their child's education.

Not all of the rich have worked hard for their money. Large amounts of those who send their children to private schools have never done anything to deserve their wealth, they have simply inheritied it. Why do their children deserve a better education than anyone else's children?  
 
Education is indeed a wothy cause and that is why we should not penalise those who cannot afford to pay. Just as those many of those who are rich have not done any to deserve their wealth neither have those who are poor ever done anything do deserve being poor, many are poor because of inability to work - maybe a longstanding illness which rendered them incapable of studying or working. Consider a teenage mother, should she be penalised because she did the what she thinks is the morally right thing in not having her baby aborted, which meant that she couldn't work and therefore won't be able to afford a better standard of education for her child.