In what sense is the Pope infallible? does that means that he is perfect? inerrant?
Papal infallibility means that the Pope is protected from error when he “proclaims by a definitive act a doctrine pertaining to faith or morals” (Catechism, 891). This does not mean that he is impeccable (incapable of sin) or inerrant (incapable of error).
For more on this see Papal Infallibility.