PS The reason why we have a doctrine of infallibility is that popes are not always correct in some ways. People are very confused on this point. From the good, old CE again.
http://www.newadvent.org/cathen/07790a.htm
“…for an ex cathedra decision it must be clear that the pope intends to bind the whole Church. To demand internal assent from all the faithful to his teaching under pain of incurring spiritual shipwreck (naufragium fidei) according to the expression used by Pius IX in defining the Immaculate Conception of the Blessed Virgin. Theoretically, this intention might be made sufficiently clear in a papal decision which is addressed only to a particular Church; but in present day conditions, when it is so easy to communicate with the most distant parts of the earth and to secure a literally universal promulgation of papal acts, the presumption is that unless the pope formally addresses the whole Church in the recognized official way, he does not intend his doctrinal teaching to be held by all the faithful as ex cathedra and infallible.”