Infallibility is not sinlessness

Question: Earlier popes had children by mistresses, obviously committing a sin against their vows of celibacy. Pope John Paul II fell and broke his hip and Pope Benedict XVI recently fell and broke his wrist. Doesn't this prove that the popes are fallible?

A frequent misrepresentation of the teaching about Papal infallibility is that it means that the Pope cannot sin or make a mistake. THAT MISCONCEPTION IS WRONG. Pope can and have fallen.

Infallibility does not mean that the Pope or any of our leaders are impeccable or perfect, just as it does NOT mean that the Scripture writers such as Solomon, Matthew, Mark, or Paul were impeccable or perfect so they could write infallible Scripture. Solomon was indeed infallibly when he wrote Proverbs, Song of Solomon, Wisdom, and some Psalms, yet later fell into idolatry and polygamous marriages with foreigners (1 Kings 11:1-8). 

Paul mistakenly commissioned Demas, who deserted his ministry for worldly gain (2 Timothy 4:9), yet Paul's writings are still infallible. Paul had corrected the first Pope, Peter but that doesn't mean we consider his writings (First and Second Peter) fallible. Peter made mistakes as do popes. Mark failed Paul (Acts 15:37-40) but his Gospel is still infallible. Committing sin and making mistakes doesn’t keep the Holy Spirit from gifting an individual with  infallibly.

Christ knew that in his Church there would be weeds mixed in with the good wheat (Matthew 13:24-30), that some Church leaders would cause scandals (Matthew 18:5-9). Yet we can still hear and obey Christ in them (2 Corinthians 5:19,20). Infallible teaching authority guarantees that the authenticity of the truth necessary for salvation.