What is your understanding of papal infallibility?
Whatever it is it's apparently inadequate. I always regret afterward stepping into these theological and/or religious discussions and I apologise in advance for being out of my depth.
But to answer your question more adequately, my understanding is mostly based on "hearsay" from Roman Catholic friends and classmates growing up of what they were taught in Catechism classes, and with former (i.e. brought up Catholic) Roman Catholics who are now members of the church I and my family chose years ago to belong to (Disciples of Christ).
But speaking as someone with a fairly solid education and degree in History, the structure of the Catholic Church has long struck me as the sole remaining example of rule by a King's divine right with the Pope in the position of unquestionable arbiter between Man and God. If you question the Bishop of Rome you are questioning God.
The immense trappings of Medieval wealth and power one sees in a place like St. Peter's make a Czarist palace look like a country shack in comparison. Having been in both places I think I am qualified to observe, compare, and comment. And I understand why the Church is this way. After all, it was in place to supplant, took on, and retain many of the forms and trappings of Imperial Rome. Some of that obscures the fact that Catholics and Protestants agree on nearly all the basics as outlined in scripture, most importantly that *Jesus the Christ was and is exactly Who He said He was*.
PS: I don't object to the "trappings". I'm as susceptible to a sense of awe and majesty as anyone. Bottom line is I don't need it. Accepting literally, and trying with a frail human brain, to come to grips with *this* fact is quite mind blowing enough for me.