When people use the "think of the children" argument, they are usually talking about the hypotheticals. "Think of the children" when you let guns or drugs in the neighborhood. "Think of the children" when you legalize prostitution.
In this instance however, it is think of this very specific child. There is no hypothetical child here who might be harmed. There is a real, actual child who will lose her ability to communicate if this app is pulled off and remotely deleted from her iPad.