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
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
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
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
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)