When he relies on his granted authority to teach for the Church rather than natural law and evidence. Reason gives you absolutes. Authority is always relative to your position or group, the delusions of Pio Nono aside. If you want to find what a nutcase he was thought to be, read Papal Sin by Garry Wills, however I can make up my mind about Nono by reading his pietistic rants. He and Pius X have been overcome by the advance of Catholic scholarship, Vatican II and the current Holy Father. Your continuing to argue these points reminds me of the Black Knight in Monty Python’s Search for the Holy Grail. You’ve got a bit of a flesh wound (your legs are gone).