Not only would i never send MY child to a private school, i largely disagree with others sending their children to private schools.
There can be no equality in a society which allows for consumers to pay for healthcare, education and the like. If all is provided by the state, then those who are lesser off will not suffer, and everyone can be equal.
I would not send my child to a private school. Not because I don't think they are better than public schools, but because the idea of private schools is wrong. Paying money to get your child a better education is against an equal society. It makes it more likely that poverty and low-income will pass on through the generations, making it harder to break out of the cycle of being poor and uneducated. Everyone should have an equal opportunity to do well in the society.