Put it this way:
- In the year 2000 the USA army existed
- In that year it had Cruise missiles
Bearing that in mind - what (if anything) is wrong with this ?
- In 1900 the USA army existed
- It is the army of the nation that had Cruise missiles
- Therefore, the US army had Cruise missiles in 1900.
The logical form may be invalid. The point should be clear enough: that one cannot conclude from the existence of a quality X in a subject Y in the present, that subject Y must have had quality X in the past.
It does not follow that because certain persons are the successors of St. Peter, all the qualities predicable of them, must be true of him. Otherwise, we would have to reason that St. Peter, one of whose successors is a Bavarian German, must himself have been a Bavarian German. Nor can we reason that because the present Pope was a professor of theology some time before becoming successor of Peter, so must Peter have been.
Some things are essential to Popes for them to be Popes - other things are not. And it does not follow that because they must observe an ecclesiastical law of clerical continence, even before becoming Pope, he too had to: because clerical continence is not essential to the clergy, whether the cleric become Pope or not - if it were, no man who had been married could ever have been ordained.
Peter was an Apostle - he was not a Pope. His function in the Church is continued, but not his vocation to the Apostolate. That was for the foundation of the Church only, not for her continued life. There can no more be a continued Apostolate, than there can be a continued institution of the Sacraments, or a continued Crucifixion. Many things in the Church are unique & unrepeatable - the vocation of the Apostles & their Apostolic labours, are among them. As is the function of Peter in the Church. The Apostolate is a bigger thing than the Papacy - Popes are bishops, & bishops are so far from being Apostles that they inherit part only of their vocation.
What continues, is the application & manifestation & unfolding & fruition of the unique & unrepeatable things: so the Petrine function continues, in a different form. As such, it has taken a variety of forms throughout the history of the Church - without any implication that because later men who exercised it were (for example) bishops of Rome before ever the Papacy developed, Peter too must have exercised the same function in the same way. That would be like supposing that because Pius IX wore the triple tiara & offered Mass in Latin, Peter must have. Which nobody believes.