This infallibility extends as far as the deposit of divine Revelation itself. Sadly, this doctrine is but another tradition of men that contradicts Scripture. The Bible declares that all people are sinners. To fulfill this service, Christ endowed the Church' s shepherds with the charism of infallibility in matters of faith and morals. It is important to understand that God did not declare these people to be infallible, other sinful men did.
Scriptures overflow with stories of sinful people.
Even those whom God used the most were sinners. The Apostle Paul and all the other apostles were sinners. Here is another tradition of men that raises more questions than it answers. Please don't blindly accept this Catholic doctrine as truth.