The answer to the original post is primarily because today’s schools often have many dangers to our faith, and past popes have repeatedly warned us about this. Some examples:
The Church cannot approve schools which exclude religion from the curriculum, both because religion is the most important subject in education, and because she contends that even secular education is not possible in its best form unless religion be made the central, vitalizing, and co-ordinating factor in the life of the child. The Church, sometimes, tolerates schools in which religion is not taught, and permits Catholic children to attend them, when the circumstances are such as to leave no alternative, and when due precautions are taken to supply by other means the religious training which such schools do not give. She reserves the right to judge whether this be the case, and, if her judgment is unfavourable, claims the right to forbid attendance" (Letter of Gregory XVI to Irish Bishops, 1831).
“…Those parents who allow their children to frequent schools where it is impossible to avoid the loss of souls… according to Catholic moral teaching, such parents, should they persist in their attitude, cannot receive absolution in the Sacrament of Penance.” Instructions Of The Holy Office To The Bishops Of The U.S., Pope Pius IX, 1875
“It is, then, incumbent on parents to strain every nerve to ward off such an outrage, and to strive manfully to have and to hold exclusive authority to direct the education of their offspring, as is fitting, in a Christian manner, and first and foremost to keep them away from schools where there is risk of their drinking in the poison of impiety” Sapientiae Christianae, Pope Leo XIII, 1890
“Obviously the need of this Christian instruction is accentuated by the decline of our times and morals. It is even more demanded by the existence of those public schools, lacking all religion, where everything holy is ridiculed and scorned. There both teachers’ lips and students’ ears are inclined to godlessness. We are referring to those schools which are unjustly called neutral or lay. In reality, they are nothing more than the stronghold of the powers of darkness.” Editae Saepe, Pope St. Pius X, 1910