The Catholic Church makes the claim because Jesus founded a Church on Peter (Matt 16:18), which persists today. The interpretation of Scripture in the Church is never down to what one man has to say, but is rather based on the whole of Tradition received through the Apostles and carried forth by the Church Fathers. The Bible is a liturgical document and cannot be separated from Tradition any more than you could separate say, stereo instructions from the actual physical device. Sola Scriptura is a heresy because without that interpretive tradition, all one is left with is a series of documents without historical or spiritual reference. Hence why everything from the Catholic and Orthodox Churches to (((Joel Osteen))) cannot be considered "Christian", because there is no single voice. Granted, even within the Catholic Church there is debate on certain interpretations of some passages, but the overall message is one of persistant belief in the same thing for millenia (namely that one must have the sacraments to be saved).