How could the Church *not *be infallible? God loves us. He wants us to know his revelation completely and without error, and with the assurance that there isn’t even the possibility of error in what we are taught. If God did not protect the Church from teaching error, we could not know for sure that anything the Church teaches is true.
Do you believe in the inspiration and inerrancy of the Bible? If so, why? You believe them because you were taught. The Bible cannot authenticate itself. As a matter of fact, we cannot know for sure that the Bible is inspired and inerrant unless an infallible teacher tells us so.
Neither can we believe in inspiration without believing in inspired persons. The Bible did not come out of nowhere; it was written down by human authors under the inspiration of the Holy Ghost. Why cannot the Church’s teachings be taught, developed, and expounded by the successors of the Apostles, under the guidance of the Holy Ghost? If they cannot, then we cannot know what the Bible means.
But this isn’t just a theory which stands to reason; Our Lord Himself said it–He who hears you hears Me (Lk 10:16), etc.