This is the way I see it, or rather, how our parish priest explained it.
Jesus couldn’t be around forever. He had to go back to Heaven at some point, so therefore He needed somebody to continue His work. At first this was Peter and the other apostles. But then, as we all know, their lives are limited as well, so they, just as Jesus did for them, had to find their replacements for when they died. This is the beginning of what we now know as Holy Orders.
As far as the Infallibility part, the Pope, unlike Jesus, needs help. That’s why he has all those Cardnials to advise him on things, just as the President has Congress to advise him. I would imagine that few, if any infallible decisions were made solely by the Pope himself. These decisions were made after much discussion and information sharing. Now that I think about it, maybe the only reason Jesus had apostles to begin with was simply to set an example for us to show us how things should be done.
I also think that if a wrong decision is made, there’s no law that says you can’t go back through the proper channels to make that decision right.