My guess is that the Mormon asked this because it is the practice of the Mormon church that one of the LDS church’s Quorom of the Twelve Apostles succeeds the president of the church. This is what happened when LDS President Gordon B. Hinckley recently died and was succeeded by the president of the Quorom, Thomas S. Monson.
Ultimately, we don’t know why Peter was not succeeded by another original apostle, but we might speculate as to reasons. Here are a couple of possibilities:
1. If an original apostle had succeeded Peter, later Christian generations might have thought such a succession was
necessary for the continuation of the papacy and then erroneously thought the papacy defunct at the death of the last original apostle.
2. Original apostles had unique gifts that were not passed down to the successors of the apostles. Had an original apostle succeeded Peter, later Christian generations might have erroneously assumed that those unique gifts were passed on to either Peter’s successor specifically or to the successors to the apostles generally.
In any event, the bottom line is that the office of the papacy, unlike the office of presidency of the LDS church, does not require that the pope be an apostle, original or otherwise.
