Then there should be a list of infallible teachings.
It’s redundant. Because then we would need an infallible affirmation of that list. And then an infallible affirmation of that affirmation. Etc. Ultimately, we know that everything that there is no error within the Catechism of the Catholic Church that is doctrinal, so you can start there. Ultimately, when the Church says that whatever she teaches in regards to faith and morals is infallible, you can bet that means that it’s every single one.
It’s like a fortune teller predicting a 1000 things and saying her some of predictions are infallible and when a prediction comes true she says “look, that was an infallible prediction” whereas if it doesn’t come true then it is merely a fallible prediction.
But the difference is that we’re not predicting anything. We’re going and saying that, "this teaching is authoritative and infallible (completely protected from error) because we have been taught this from our predecessors, who were taught it from their predecessors, etc. We’re not gambling, here. When we say that something is infallibly taught, such as the intrinsic evil of Abortion or Artificial Birth Control, then it’s intrinsically evil. Both have been taught in this way before someone pronounces it, and after someone pronounces it. If you are referring to statements by Popes, then we must realize that it’s
anything that is within the framework of faith and moral. This limits a lot of possibilities for which statements have been made infallible and which haven’t. Remember, we’re working with the past here, not the future. To say that it’s like working with the future, that we’re making an “infallible prediction” and that out of a 1000 some of them are and some are not, is fallacious, because we’re not working with the future here. We’re not saying, "some of the Pope’s statements on faith and morals in regards to murder, communism, abortion, Our Lord Jesus, The Blessed Virgin, the Scriptures, etc. are infallible and others are not. When the Pope says, “Jesus is the Lord our God who takes away the sin of the world”, he is protected from saying “Jesus is just a man” by the Holy Spirit. This is what makes him infallible. He is protected from error. This isn’t just some of the time, it’s all of the time. We know what subjects will be authoritative and which ones won’t. For example, science, I am a theistic evolutionist. I know that some on this forum are YEC and OEC, etc. Yet none of our opinions on evolution or on how creation developed after point zero, the original point of creation, because we all agree that it was God, the Lord Almighty, who created the Heavens and the Earth Ex Nihilo, who is and was and always will be I AM. Whatever we think doesn’t matter when we consider this, because it is a doctrine we all accept as infallible, authorative teaching. The Church, however, does not have the authority to dictate what is true and untrue scientifically. That is beyond their authority. This is the point you must understand, that the Church isn’t saying that they are 100% on everything at all times every day. There is specific criteria.