The pope teaches infallibly when he invokes his charism of infallibility.
Papal infallibility has only been invoked a handful of times in the past 150 years.
There are other levels of Church Teaching of various degrees of certainty and authority. There also exists a hierarchical Church structure, including Church courts.
Church courts are like military tribunals or our judicial system. Their findings are not infallible, but they must be followed.
"If he will not listen to the Church, treat him as a pagan." --Jesus
It sounds as though you have bought into the Black Legend of the Inquisition created by Protestant revolutionaries.
BBC Video: The Myth of the Spanish Inquisition
National Review: The Real Inquisition: Investigating the Popular Myth
Historians are ahead of the public. The Black Legend was discredited about 20 years ago with the publishing of trial documents from the Tribunals.
Conventional wisdom is still catching up.
Got a whole tote bag full of dissonance you can pull out to defend the catholic religion. If catholiciism were Christianity you would need that gunnysack.