I believe everything the creed says, but why must I also believe in papal infallibility?

Because, if you believe the creed to be the essential teaching of our Catholic faith, you therefore “believe in one, holy, catholic and apostolic Church.” When that Church, with the apostolic authority described by the creed, promulgates dogmas (such as the dogmas concerning Mary or the infallibility of the pope), it is declaring that this teaching is something we have received, implicitly or explictly, from the apostles. You therefore are bound to believe it precisely because of what the creed teaches about the Church. You cannot pit the creed against the Church’s teaching of doctrine.