Here are a few points from Canon Law that are relevant to the topic:
Can. 793 §1. Parents and those who take their place are bound by the obligation and possess the right of educating their offspring. Catholic parents also have the duty and right of choosing those means and institutions through which they can provide more suitably for the Catholic education of their children, according to local circumstances.
§2. Parents also have the right to that assistance, to be furnished by civil society, which they need to secure the Catholic education of their children.
Can. 794 §1. The duty and right of educating belongs in a special way to the Church, to which has been divinely entrusted the mission of assisting persons so that they are able to reach the fullness of the Christian life.
Can. 798 Parents are to entrust their children to those schools which provide a Catholic education. If they are unable to do this, they are obliged to take care that suitable Catholic education is provided for their children outside the schools.
Can. 800…§2. The Christian faithful are to foster Catholic schools, assisting in their establishment and maintenance according to their means.
Can. 803…2. The instruction and education in a Catholic school must be grounded in the principles of Catholic doctrine; teachers are to be outstanding in correct doctrine and integrity of life
BTW, I went to Catholic school and it was a great experience. I want my children to go to Catholic school, especially because in public school, for the most part, I will have my hands tied if they teach them something against our faith, but in Catholic school I can do something about it.