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Families who sent their children to private schools should not be required to pay taxes that support the state education system. To what extent do you agree or disagree with this statement?

Some people argue that government should not require parents whose children enrolling private schools to pay taxes for state school maintenance. I completely disagree with this opinion.
In my opinion, everyone has to fulfill an obligation to support the state education system by paying taxes without any exception. This movement could effectively ensure sustainable equality among different classes in the society. For example, the rich or the poor people should spend the same amount of money through the government's tax system to upgrade state educational environment. Furthermore, if there was no support from the community, the government would struggle to retain the state-school quality as a result of huge cost. It is clear that most families who sent their children to private schools are relatively wealthy, which makes them be sustainable to mutually share the weight of cost.
On the other hand, allowing families with children who are sent to private educational system to pay no taxes means that this move accidentally encourage academic imbalance in quality to arise between private-school and public-school students. The children studying at a less favorable environment of state schools tent to be less qualified or competitive in comparison with the other ones in the job market. At the same time, there will be a remarkable influx of young people applying for private schools growing with the passage of time because of the attractively good educational conditions. Finally, I doubt that state schools seem not to be appealing enough to keep good teachers working.
In conclusion, I believe that it is compulsory for everyone, especially families with children studying at non-public education system to competitively improve state schools by paying taxes.