Exposure to the “dark side” to prepare to refute it is NOT, IMHO, a bad idea.
They get plenty of that without the involvement of catholic schools, believe me.
A protestant friend of mine uses your argument all the time -- equally fallacious there. In fact, he used it to say his kids might as well go to a public school rather than a faith-oriented school. That's not a line of reasoning I'm going to engage in. Why not just go to a known Satanic school to prepare for the very worst?