Hi Emilia,

Thanks for your question.

You seem to have a misunderstanding of what infallibility is.

It is not impeccability.  That is, it does not refer to the Pope's personal Holiness.

Infallibility is a gift which protects the Pope from officially teaching defining error as truth in the area of faith and morals.

That does not mean that he himself will not violate the same truth he teaches.

For instance, in Acts 15, St. Peter definitively declares that Gentiles did not have to keep the Kosher Laws or be circumcised in order to become Christians.

Later, we read in Galatians that he violates, at very least, the spirit of this infallible declaration. St. Paul writes that he had to rebuke Peter for not eating at the same table with Gentiles, so as to keep the Jewish believers happy.

In granting his daughter six annulments, Alexander was not teaching on annulments, though he could have been breaking the Church's doctrine on this issue.

As for Savaonarola, again, Alexander seems to be guilty of a pretty serious personal sin!!
The execution of Savaonarola, along with the later execution of John Huss, was part of the sad background of the Protestant Rebellion.

As the Catechism says (CCC 817), anytime there is division, there is most likely sin by men on both sides of the issue. This incident is truly a black eye on the face of Church history. However, this horrible execution is not covered by papal infallibility either as we distinguish between official teachings re-affirmed by the Pope under the guidance of the Holy Spirit from his personal holiness. (e.g. his personal actions or behavior)

God Bless,

John DiMascio