Ryan believes if his son continues to attend a religious school, it will attempt to indoctrinate his son into a belief system that he as a parent rejects.Many Protestants send their kids to Catholic schools without fearing they will be "indoctrinated" into a religion they don't agree with. I know many Jewish kids attended my school, which had daily chapel services which featured Christian hymns and New Testament readings.
Kagin said part of Kentucky’s constitution reads, "Nor shall any man be compelled to send his child to any school to which he may be conscientiously opposed."
I think "man" here really means "person." The mother has rights too.
But he is going to try to go by a strict interpretation of the constitution. Man being a human male, not person. So his wishes as father top his ex-wife's wishes as mother.
The other part of this that I did not see if who is paying for the school. If Mr. Ryan is paying all or a large part of the cost of sending his son to Catholic school this may be a reason he is so adamant his child will not attend.