The rock that I foundered on as a Protestant was the question of authority. Here’s what the Bible says about the Apostles:
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Jesus will always be with them. (Matthew 28: 20)
The Holy Spirit will guide them into all truth, and will be with them always. (John 14:16-17; 15:26; 16:13)
(Implicit in this is the assumption that there is truth that they have not yet been taught. (explicit in John 16:12))
They speak with the authority of God. (Matthew 10:20; Luke 10:1; Luke 10:16)
They will remember everything Jesus taught them. (John 14:16-18, 26; Luke 21:33)
They will never teach erroneous doctrine. (John 17:17-19)
They be one in the doctrine they teach (John 17:20-23)
They have to power to forgive sin. (John 20:21-23)
God will give them whatever they ask for in Christ’s name, and the fruit they bear will remain. (John 15:16)
(‘Fruit’ here would mean the churches they founded, the Christian communities they started as they traveled. Expand on this; the biblical and extra-biblical evidence (Book of Revelations praising the doctrinal faithfulnes of specific churches, writings of the church fathers, agreement in doctine among widely-flung churches, lack of discord regarding key doctrines) indicates that Catholic teaching is faithful to the Apostles, as Jesus in this verse said it would be.)
Peter has a pre-eminent place among the Apostles. (Matthew 16:17-19
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Once I got this into my head and really grappled with it, and discovered that the earliest Church Fathers, who learned the faith directly from the Apostles, were obviously Catholic, then I knew I had to become a Catholic myself. The alternative was to conclude that Jesus was wrong in John 15:16.