Jesus is Infallible, Popes not so much.
1)First of all my reply will begin to Rodm. Yes Jesus is infallible he is also the second person of the Blessed Trinity. The trinity obviously includes The Father, the Son, and the Holy Spirit.
As Catholics we profess that the Holy Trinity is consubstantial. This simply means that what belongs to one Divine Person of the Trinity belongs just as much to each other. Just as much as the Father is Omni-potent (Is all powerful) and omniscient (knows everything) the Son Jesus Christ and the Holy Spirit share in these natures and attributes just as much as the Father does.
As Catholics we profess that the Pope is the Vicar of Christ. A Vicar is simply a representative which acts for another. In the Old Testament King David would hand over his keys (authority) over to a vicar while he went of to war. At the moment that King David would return he would get back the keys (authority). The pope is no different. He is the Vicar of Christ. In other words he acts for Christ and is given the same authority that Christ has as well the keys (authority).
The pope is infallible when he meets the conditions of Ex Cathedra as stated in the article 1) He talks to the whole Church 2) He talks with authority as the Pope (Vicar of Christ) 3) talks regarding faith and morals
Does it is only when the pope talks Ex Cathedra that Catholics declare that the pope is infallible. This is so because he is guided by the Holy Spirit at the moment of doing just as much as the bible is free from error as it is written by humans under the inspiration of God through the Holy Spirit. (The Holy Spirit prevents error in the bible)
2)My second reply is to Popman
I don’t know if you are a Christian. As a Christian we believe that the bible is the inerrant word of God. Why? Because it was written by humans under the inspiration of God by means of the Holy Spirit as stated in the end of my first reply to Rodm. Where not the human authors who wrote the bible born of sin? Yes they were, but they were also protected from error by this same inspiration of God preventing error. The bible just as Jesus has two natures, a human and a divine. It is human because it was written by humans (of which were born with original sin) yet the bible is also the Word of God (Divine Nature)
The pope is born of original sin, but because he is protected by God through the Holy Spirit just as the writers of the bible were. It is only though in his Ex Cathedra statements that the pope is infallible (protected by God from teaching error)