So, while people in the church (including bishops and popes) can make mistakes, we can put our trust in the Catholic Church because Jesus (who was perfect) did not make a mistake when he said the gates of hell would not prevail against his Church.
I'll put my faith in God. The Pharisees thought they were infallible, too, and look what Jesus had to say to them. An infallible church would not have sold indulgences, to use just one example.