It is a dogma of the Catholic Church that the Church is divinely kept from the possibility of error in her definitive teaching on faith and morals.

Definition of “Infallibility” from “A Catholic Dictionary”, 1951: "This infallibility resides (A) in the pope personally and alone; (B) in an ecuмenical Council subject to papal confirmation (these infallibilities are distinct but correlative); (C) in the bishops of the Church, dispersed throughout the world, teaching definitively in union with the pope. This is not a different infallibility from (B) but is the ordinary exercise of a prerogative (hence called the "ordinary magisterium") which is manifested in a striking manner in an ecuмenical Council. This ordinary magisterium is exercised by pastoral letters, preaching, catechisms, the censorship of publications dealing with faith and morals, the reprobation of doctrines and books: it is thus in continuous function and embraces the whole deposit of faith."

It's hard for me to understand why logic goes out the window when the topic of infallibility comes up.  The church is run by rules - Divine Law, canon law, and doctrine.  If you don't follow the rules, then you don't have the intended outcome. 

7 Sacraments = require proper matter and form.
Confession = 5 required acts to be forgiven.
Holy Mass = 3 principal parts of Offertory, Canon and Communion.
Reception of Communion = 3 requirements - State of Grace, fasting, age of reason/proper disposition.
Infallibility per V1 = Apostolic authority, matter of faith/morals, binding of the faithful, to believe with certainty of faith.

But, it seems for some, that when infallibility comes up, their understanding of it is like a spiritual superpower which is used when the pope decides to use it and it's hard for them to understand.  They'll say:  "When the pope and bishops get together and teach".  Or "When the pope is speaking of faith and morals".  Or worse, "When the pope issues an encyclical."

All of the above situations are too general.  All of the above COULD be infallible IF the proper REQUIREMENTS are met.  If all the requirements aren't met, then such actions aren't infallible.   

2. ecuмenical councils under the headship of the pope;

Vatican II?

"All those things are to be believed by divine and Catholic faith which are contained in the written Word of God or in Tradition, and which are proposed by the Church, either in solemn judgment or in its ordinary and universal teaching office, as divinely revealed truths which must be believed."

Aw shucks, LoT, you always seem to miss the key passage here.  BoD is clearly not divinely revealed.

Silver lining: he states that he won't communicate with those who don't pretend to/respect him, so there's at least one "shut up" button.