Because she is the only Church that Christ established. The early Church taught the exact same things that the Catholic Church teaches today, because she is one and the same. http://www.staycatholic.com/early_church_fathers.htm
Yes, I know what "kepha" means, a massive rock structure. Before you say what everyone else always says, of course it says "Petros" (not "lithos") in Greek, it's a masculine noun because Jesus would not have given Peter a feminine name such as "Petra", the meanings of the two words had no distinction in Koine Greek. You act like the Church that spoke Greek for centuries understands it less than you do.
The Church either existed indestructibly for two-thousand years or it is all a lie. There is no in-between.